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arxiv: 2605.18030 · v1 · pith:4UF3DGLUnew · submitted 2026-05-18 · 📊 stat.ME

A robust nonparametric test for spatial isotropy in lattice data

Jana Gierse , Roland Fried This is my paper

Pith reviewed 2026-05-20 01:08 UTC · model grok-4.3

classification 📊 stat.ME
keywords spatial isotropyvariogramrobust testblock permutationlattice datanonparametric testoutliers
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The pith

Block permutation with robust variogram estimators maintains the nominal significance level for spatial isotropy even under strong dependencies and outliers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a robust nonparametric test for whether spatial data on a regular two-dimensional grid exhibit the same properties in all directions. It modifies an existing subsampling procedure that compares variogram estimates at equal distances but in different directions, replacing ordinary estimators with robust versions derived from univariate or multivariate scatter. A new block-permutation resampling scheme is introduced in place of subsampling. This combination keeps the test's type I error rate at the nominal level when observations are strongly autocorrelated and when isolated or block contamination is present, as verified in simulations and illustrated on Landsat 8 imagery.

Core claim

The block permutation test that uses robust scatter-based variogram estimators to compare directional differences at equal lag distances maintains the nominal significance level under strong spatial dependence and remains insensitive to isolated or contiguous outlier blocks.

What carries the argument

Block permutation resampling applied to directional differences of robust variogram estimates computed via univariate or multivariate scatter estimators.

Load-bearing premise

The observations lie on a two-dimensional regular grid and any contamination consists of isolated points or contiguous blocks whose effect can be mitigated by robust scatter estimators.

What would settle it

Simulate isotropic lattice data with strong dependence and inserted block outliers, then verify whether the empirical rejection rate of the proposed test under the null stays close to the nominal significance level.

read the original abstract

This paper proposes a robust test for assessing isotropy based on the variogram of spatial data on a two-dimensional regular grid. The test is based on the non-robust subsampling test for isotropy of Guan et al. (2004), which uses the idea of comparing variogram estimates in diff erent directions at the same distance. The robust test employs robust variogram esti- mators which are based on estimators of univariate or multivariate scatter and perform well in the presence of isolated or block outliers. Additionally, a diff erent resampling method, called block permutation, is proposed. Compared with the subsampling test, the block per- mutation test maintains the signifi cance level even for strong dependencies in the data and is robust to outliers. The methods are illustrated by an application to Landsat 8 satellite data, where outlier blocks may occur due to, for example, clouds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes a robust nonparametric test for spatial isotropy in two-dimensional lattice data. It extends the subsampling-based test of Guan et al. (2004) by replacing classical variogram estimates with robust versions derived from univariate or multivariate scatter functionals (to accommodate isolated or block outliers) and introduces a block-permutation resampling procedure that is asserted to maintain the nominal significance level under strong spatial dependence.

Significance. If the level control and robustness claims can be substantiated, the procedure would supply a practical tool for isotropy testing in contaminated spatial datasets such as satellite imagery, where conventional methods can be distorted by outliers or long-range correlation.

major comments (2)
  1. Abstract: the claims that the block-permutation test 'maintains the significance level even for strong dependencies in the data' and 'is robust to outliers' are presented without any simulation results, power curves, or explicit error-rate derivations, so the central performance assertions cannot be verified from the given text.
  2. Description of the robust variogram estimators: the construction relies on scatter functionals (MCD, S-estimators, etc.) whose consistency and breakdown-point results are standard only under i.i.d. or weak-dependence regimes; no additional regularity conditions on the covariance function or separate consistency argument are supplied for the long-range dependence structures (e.g., Matérn with small smoothness) that the block-permutation scheme is intended to accommodate.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the opportunity to clarify aspects of our work. We respond to each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: Abstract: the claims that the block-permutation test 'maintains the significance level even for strong dependencies in the data' and 'is robust to outliers' are presented without any simulation results, power curves, or explicit error-rate derivations, so the central performance assertions cannot be verified from the given text.

    Authors: We appreciate the referee highlighting the need for clearer support of these claims in the abstract. The full manuscript includes simulation studies (Section 4) that examine the block-permutation procedure under strong spatial dependence, including Matérn covariances with small smoothness parameters, and under both isolated and block outliers. These experiments show that the test maintains the nominal significance level in settings where the original subsampling approach of Guan et al. (2004) does not, and that the robust variogram estimators preserve this property in contaminated data. We will revise the abstract to include a concise reference to these simulation results. While we do not supply closed-form error-rate derivations, the block-permutation scheme is justified by its preservation of the spatial dependence structure within blocks, analogous to established block-resampling methods; the numerical evidence provides the primary validation. revision: partial

  2. Referee: Description of the robust variogram estimators: the construction relies on scatter functionals (MCD, S-estimators, etc.) whose consistency and breakdown-point results are standard only under i.i.d. or weak-dependence regimes; no additional regularity conditions on the covariance function or separate consistency argument are supplied for the long-range dependence structures (e.g., Matérn with small smoothness) that the block-permutation scheme is intended to accommodate.

    Authors: We agree that the standard consistency and breakdown-point theory for MCD, S-estimators, and related scatter functionals is typically stated under i.i.d. or weakly dependent observations. In the manuscript these functionals are applied to compute directional variogram estimates on lattice data, with the block-permutation resampling used to handle strong dependence. We do not supply a separate consistency argument under long-range dependence in the current version. In the revision we will add a brief discussion noting that additional regularity conditions on the covariance function (for example, suitable mixing or integrability conditions compatible with the Matérn class) would be required for a full theoretical extension, while emphasizing that the practical performance is supported by the simulations conducted under precisely those long-range models. revision: yes

Circularity Check

0 steps flagged

No significant circularity; extends external subsampling test with independent robust estimators and block permutation

full rationale

The derivation begins from the non-robust subsampling procedure of Guan et al. (2004), an external reference, and introduces new robust variogram estimators constructed from univariate or multivariate scatter functionals together with a block-permutation resampling scheme. These additions are defined directly from standard robust scatter literature and a new resampling idea; no equation equates a claimed performance guarantee (level maintenance under strong dependence or outlier robustness) to a fitted quantity or self-referential definition inside the paper. Central assertions rest on the algebraic construction of the estimators and the permutation mechanism rather than on any self-citation chain or ansatz smuggled from prior author work. The manuscript therefore remains self-contained against external benchmarks and does not reduce its results to tautological inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard spatial lattice assumptions and the characterization of outliers as isolated or block-type; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Spatial observations are recorded on a two-dimensional regular grid.
    Explicitly stated as lattice data in the abstract.
  • domain assumption Outliers appear either as isolated points or as contiguous blocks.
    Mentioned as the motivation for robustness and illustrated by clouds in satellite data.

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Works this paper leans on

149 extracted references · 149 canonical work pages

  1. [1]

    A note on robust and non-robust variogram estimators , volume =

    Sueli Aparecida Mingoti and Gilmar Rosa , doi =. A note on robust and non-robust variogram estimators , volume =. Revista Escola de Minas , keywords =

    work page

  2. [2]

    Combining robustness with efficiency in the estimation of the variogram , volume =

    Hilário Miranda and Manuela Souto de Miranda , doi =. Combining robustness with efficiency in the estimation of the variogram , volume =. Mathematical Geosciences , keywords =

    work page

  3. [3]

    Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator , volume =

    Christophe Croux and Gentiane Haesbroeck , doi =. Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator , volume =. Journal of Multivariate Analysis , keywords =

    work page

  4. [4]

    Minimum covariance determinant , volume =

    Mia Hubert and Michiel Debruyne , doi =. Minimum covariance determinant , volume =. Wiley Interdisciplinary Reviews: Computational Statistics , keywords =

    work page

  5. [5]

    Pison and S

    G. Pison and S. Van Aelst and G. Willems , doi =. Small sample corrections for LTS and MCD , volume =. Metrika , keywords =

    work page

  6. [6]

    R. W. Butler and P. L. Davies and M. Jhun , doi =. Asymptotics for the minimum covaraince determinant estimator , volume =. The Annals of Statistics , keywords =

    work page

  7. [7]

    Rousseeuw and Katrien Van Driessen , doi =

    Peter J. Rousseeuw and Katrien Van Driessen , doi =. A fast algorithm for the minimum covariance determinant estimator , volume =. Technometrics , keywords =

    work page

  8. [8]

    Rousseeuw , doi =

    Peter J. Rousseeuw , doi =. Multivariate Estimation with high breakdown point , url =. Mathematical Statistics and Applications Vol. B , pages =

    work page

  9. [9]

    Genton , doi =

    Marc G. Genton , doi =. Spatial breakdown point of variogram estimators , volume =. Mathematical Geology , keywords =

    work page

  10. [10]

    Hawkins , doi =

    Noel Cressie and Douglas M. Hawkins , doi =. Robust estimation of the variogram: I , volume =. Journal of the International Association for Mathematical Geology , keywords =

    work page

  11. [11]

    R. M. Lark , doi =. Estimating variograms of soil properties by the method-of-moments and maximum likelihood , volume =. European Journal of Soil Science , pages =

    work page

  12. [12]

    Lark , doi =

    Murray R. Lark , doi =. Some results on the spatial breakdown point of robust point estimates of the variogram , volume =. Mathematical Geosciences , keywords =

    work page

  13. [13]

    Genton , doi =

    Marc G. Genton , doi =. Highly Robust Variogram Estimation , volume =. Mathematical Geology , keywords =

    work page

  14. [14]

    R. M. Lark , doi =. A comparison of some robust estimators of the variogram for use in soil survey , volume =. European Journal of Soil Science , pages =

    work page

  15. [15]

    Robust forecasting with exponential and holt-winters smoothing , volume =

    Sarah Gelper and Roland Fried and Christophe Croux , doi =. Robust forecasting with exponential and holt-winters smoothing , volume =. Journal of Forecasting , keywords =

    work page

  16. [16]

    Forecasting Using Robust Exponential Smoothing with Damped Trend and Seasonal Components , year =

    Ruben Crevits and Christophe Croux , doi =. Forecasting Using Robust Exponential Smoothing with Damped Trend and Seasonal Components , year =

    work page

  17. [17]

    Exponential smoothing for time series with outliers , volume =

    Tomás Hanzák and Tomáš Cipra , issue =. Exponential smoothing for time series with outliers , volume =. Kybernetika , keywords =

    work page

  18. [18]

    Phenological change detection while accounting for abrupt and gradual trends in satellite image time series , volume =

    Jan Verbesselt and Rob Hyndman and Achim Zeileis and Darius Culvenor , doi =. Phenological change detection while accounting for abrupt and gradual trends in satellite image time series , volume =. Remote Sensing of Environment , keywords =

    work page

  19. [19]

    Spatio-temporal change detection from multidimensional arrays: Detecting deforestation from MODIS time series , volume =

    Meng Lu and Edzer Pebesma and Alber Sanchez and Jan Verbesselt , doi =. Spatio-temporal change detection from multidimensional arrays: Detecting deforestation from MODIS time series , volume =. ISPRS Journal of Photogrammetry and Remote Sensing , keywords =

    work page

  20. [20]

    Robust control charts for time series data , volume =

    Christophe Croux and Sarah Gelper and Koen Mahieu , doi =. Robust control charts for time series data , volume =. Expert Systems with Applications , keywords =

    work page

  21. [21]

    Computational aspects of robust Holt-Winters smoothing based on M-estimation , volume =

    Christophe Croux and Sarah Gelper and Roland Fried , isbn =. Computational aspects of robust Holt-Winters smoothing based on M-estimation , volume =. Applications of Mathematics , keywords =

    work page

  22. [22]

    Holt-Winters Method with Missing Observatons , volume =

    Tomáš Cipra and José Trujillo and Asunción Rubio , issue =. Holt-Winters Method with Missing Observatons , volume =. Management Science , keywords =

    work page

  23. [23]

    Cipra , doi =

    T. Cipra , doi =. Exponential smoothing for irregular data , volume =. Applications of Mathematics , keywords =

    work page

  24. [24]

    Detecting trend and seasonal changes in satellite image time series , volume =

    Jan Verbesselt and Rob Hyndman and Glenn Newnham and Darius Culvenor , doi =. Detecting trend and seasonal changes in satellite image time series , volume =. Remote Sensing of Environment , keywords =

    work page

  25. [25]

    On-demand processing of data cubes from satellite image collections with the gdalcubes library , volume =

    Marius Appel and Edzer Pebesma , doi =. On-demand processing of data cubes from satellite image collections with the gdalcubes library , volume =. Data , keywords =

    work page

  26. [26]

    Robust exponential smoothing of multivariate time series , volume =

    Christophe Croux and Sarah Gelper and Koen Mahieu , doi =. Robust exponential smoothing of multivariate time series , volume =. Computational Statistics and Data Analysis , pages =

    work page

  27. [27]

    Near real-time disturbance detection using satellite image time series , volume =

    Jan Verbesselt and Achim Zeileis and Martin Herold , doi =. Near real-time disturbance detection using satellite image time series , volume =. Remote Sensing of Environment , keywords =

    work page

  28. [28]

    Robust methods in exponential smoothing , volume =

    Jirí Michálek , issue =. Robust methods in exponential smoothing , volume =. Kybernetika , pages =

    work page

  29. [29]

    D. M. Hawkins and D. J. Olive , doi =. Inconsistency of resampling algorithms for high-breakdown regression estimators and a new algorithm , volume =. Journal of the American Statistical Association , keywords =

    work page

  30. [30]

    Rousseeuw , doi =

    Peter J. Rousseeuw , doi =. Breakdown and groups , volume =. Annals of Statistics , keywords =

    work page

  31. [31]

    Lopuhaä , doi =

    Hendrik P. Lopuhaä , doi =. Asymptotics of reweighted estimators of multivariate location and scatter , volume =. Annals of Statistics , keywords =

    work page

  32. [32]

    Lopuhaä and Peter J

    Hendrik P. Lopuhaä and Peter J. Rousseeuw , doi =. Breakdown points of affine equivariant estimators of multivariate location and covariance matrices , volume =. The Annals of Statistics , keywords =

    work page

  33. [33]

    The minimum weighted covariance determinant estimator , volume =

    Ella Roelant and Stefan Van Aelst and Gert Willems , doi =. The minimum weighted covariance determinant estimator , volume =. Metrika , keywords =

    work page

  34. [34]

    P. L. Davies , doi =. Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices , volume =. Annals of Statistics , keywords =

    work page

  35. [35]

    Periodicity detection in irregularly sampled light curves by robust regression and outlier detection , volume =

    Anita Monika Thieler and Michael Backes and Roland Fried and Wolfgang Rhode , doi =. Periodicity detection in irregularly sampled light curves by robust regression and outlier detection , volume =. Statistical Analysis and Data Mining , keywords =

    work page

  36. [36]

    Cator and Hendrik P

    Eric A. Cator and Hendrik P. Lopuhaä , doi =. Central limit theorem and influence function for the MCD estimators at general multivariate distributions , volume =. Bernoulli , keywords =

    work page

  37. [37]

    Rates of convergence for empirical processes of stationariy mixing sequences , volume =

    Bin Yu , issue =. Rates of convergence for empirical processes of stationariy mixing sequences , volume =. The Annals of Probability , keywords =

    work page

  38. [38]

    Kerry and M

    R. Kerry and M. A. Oliver , doi =. Determining the effect of asymmetric data on the variogram. I. Underlying asymmetry , volume =. Computers and Geosciences , keywords =

    work page

  39. [39]

    Kerry and M

    R. Kerry and M. A. Oliver , doi =. Determining the effect of asymmetric data on the variogram. II. Outliers , volume =. Computers and Geosciences , keywords =

    work page

  40. [40]

    Traité de géostatistique appliquée, Tome I

    Georges Matheron , pages =. Traité de géostatistique appliquée, Tome I. , year =

    work page

  41. [41]

    Rousseeuw and Christophe Croux , doi =

    Peter J. Rousseeuw and Christophe Croux , doi =. Alternatives to the median absolute deviation , volume =. Journal of the American Statistical Association , keywords =

    work page

  42. [42]

    Dowd , city =

    P. Dowd , city =. The variogram and kriging: robust and resistant estimators , year =. Geostatistics for Natural Resources Characterization. Part I , pages =

    work page

  43. [43]

    Robust estimation of (partial) autocorrelation , volume =

    Alexander Dürre and Roland Fried and Tobias Liboschik , doi =. Robust estimation of (partial) autocorrelation , volume =. WIREs Computational Statistics , keywords =

    work page

  44. [44]

    Rousseeuw , doi =

    Mia Hubert and Michiel Debruyne and Peter J. Rousseeuw , doi =. Minimum covariance determinant and extensions , volume =. Wiley Interdisciplinary Reviews: Computational Statistics , keywords =

    work page

  45. [45]

    2024 , url =

    R: A Language and Environment for Statistical Computing , author =. 2024 , url =

    work page 2024

  46. [46]

    Martin Schlather and Alexander Malinowski and Marco Oesting and Daphne Boecker and Kirstin Strokorb and Sebastian Engelke and Johannes Martini and Felix Ballani and Olga Moreva and Jonas Auel and Peter J Menck and Sebastian Gross and Paulo Riberio and Brian D Ripley and Richard Singelton and Ben Pfaff and R Core Team , title =

    work page

  47. [47]

    Clayton V Deutsch and A. G. Journel , city =. GSLIB: Geostatistical Software Library and User's Guide , year =

    work page

  48. [48]

    Martin Maechler and Peter J. Rousseeuw and Christophe Croux and Valentin Todorov and Andreas Ruckstuhl and Matias Salibian-Barrera and Tobias Verbeke and Manuel Koller and Eduardo Conceicao and Maria Anna di Palma , title =

    work page

  49. [49]

    Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields , volume =

    Martin Schlather and Alexander Malinowski and Marco Oesting and Daphne Boecker and Kirstin Strokorb and Sebastian Engelke and Johannes Martini and Felix Ballani and Olga Moreva and Jonas Auel and Peter J Menck and Sebastian Gross and Ulrike Ober and Christoph Berreth and Katharina Burmeister and Juliane Manitz and Paulo Ribeiro and Richard Singleton and B...

    work page

  50. [50]

    Computation and analysis of multiple structural change models , volume =

    Jushan Bai and Pierre Perron , doi =. Computation and analysis of multiple structural change models , volume =. Journal of Applied Econometrics , note =

    work page

  51. [51]

    Robust control charts for the mean of a locally linear time series , year =

    Sermad Abbas and Roland Fried , doi =. Robust control charts for the mean of a locally linear time series , year =. Journal of Statistical Computation and Simulation , keywords =

    work page

  52. [52]

    Neue Wege der Geodaten ­ Nutzung : Perspektiven der Fernerkundung für die Statistik , volume =

    Stephan Arnold and Sarah Kleine , journal =. Neue Wege der Geodaten ­ Nutzung : Perspektiven der Fernerkundung für die Statistik , volume =

    work page

  53. [53]

    Structural breaks in time series , volume =

    Alexander Aue and Lajos Horváth , doi =. Structural breaks in time series , volume =. Journal of Time Series Analysis , keywords =

    work page

  54. [54]

    A. J. Baczkowski and K. V. Mardia , doi =. A Test of Spatial Symmetrie with General Application , volume =. Communications in Statistics - Theory and Methods , keywords =

    work page

  55. [55]

    Bustos and Víctor J

    Oscar H. Bustos and Víctor J. Yohai , issue =. Robust Estimates for ARMA Models , volume =. Journal of the American Statistical Association , note =

    work page

  56. [56]

    Calvin , doi =

    Yongtao Guan and Michael Sherman and James A. Calvin , doi =. A nonparametric test for spatial isotropy using subsampling , volume =. Journal of the American Statistical Association , keywords =

    work page

  57. [57]

    Weller and Jennifer A

    Zachary D. Weller and Jennifer A. Hoeting , doi =. A review of nonparametric hypothesis tests of isotropy properties in spatial data , volume =. Statistical Science , keywords =

    work page

  58. [58]

    Weller , doi =

    Zachary D. Weller , doi =. Sptest: An R package implementing nonparametric tests of isotropy , volume =. Journal of Statistical Software , keywords =

    work page

  59. [59]

    Spatial Statistics and Spatio-Temporal Data , year =

    Michael Sherman , edition =. Spatial Statistics and Spatio-Temporal Data , year =

    work page

  60. [60]

    M. N. M. van Lieshout , isbn =. Theroy of Spatial Statistics , year =

    work page

  61. [61]

    Knight and Geir Kvaran , doi =

    Edward J. Knight and Geir Kvaran , doi =. Landsat-8 operational land imager design, characterization and performance , volume =. Remote Sensing , keywords =

    work page

  62. [62]

    Scaramuzza and Song Guo and Zhe Zhu and Ronald D

    Steve Foga and Pat L. Scaramuzza and Song Guo and Zhe Zhu and Ronald D. Dilley and Tim Beckmann and Gail L. Schmidt and John L. Dwyer and M. Joseph Hughes and Brady Laue , doi =. Cloud detection algorithm comparison and validation for operational Landsat data products , volume =. Remote Sensing of Environment , keywords =

    work page

  63. [63]

    Characteristics of Landsat 8 OLI-derived NDVI by comparison with multiple satellite sensors and in-situ observations , volume =

    Yinghai Ke and Jungho Im and Junghee Lee and Huili Gong and Youngryel Ryu , doi =. Characteristics of Landsat 8 OLI-derived NDVI by comparison with multiple satellite sensors and in-situ observations , volume =. Remote Sensing of Environment , keywords =

    work page

  64. [64]

    Tucker , doi =

    Compton J. Tucker , doi =. Red and photographic infrared linear combinations for monitoring vegetation , volume =. Remote Sensing of Environment , pages =

    work page

  65. [65]

    Myneni and Forrest G

    Ranga B. Myneni and Forrest G. Hall and Piers J. Sellers and Alexander L. Marshak , doi =. The interpretation of spectral vegetation indexes , volume =. IEEE Transactions on Geoscience and Remote Sensing , pages =

    work page

  66. [66]

    D. P. Roy and M. A. Wulder and T. R. Loveland and Woodcock C.E. and R. G. Allen and M. C. Anderson and D. Helder and J. R. Irons and D. M. Johnson and R. Kennedy and T. A. Scambos and C. B. Schaaf and J. R. Schott and Y. Sheng and E. F. Vermote and A. S. Belward and R. Bindschadler and W. B. Cohen and F. Gao and J. D. Hipple and P. Hostert and J. Huntingt...

    work page

  67. [67]

    Nasa , keywords =

    Landsat 8 Data Users Handbook , volume =. Nasa , keywords =

    work page

  68. [68]

    Bowman and Rosa M

    Adrian W. Bowman and Rosa M. Crujeiras , doi =. Inference for variograms , volume =. Computational Statistics and Data Analysis , keywords =

    work page

  69. [69]

    G. E. P. Box and David A. Pierce , issue =. Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , volume =. Journal of American Statistical Association , pages =

    work page

  70. [70]

    Penalized quasi-maximum likelihood estimation for extreme value models with application to flood frequency analysis , volume =

    Axel Bücher and Jona Lilienthal and Paul Kinsvater and Roland Fried , doi =. Penalized quasi-maximum likelihood estimation for extreme value models with application to flood frequency analysis , volume =. Extremes , keywords =

    work page

  71. [71]

    Detection of spatial change points in the mean and covariances of multivariate simultaneous autoregressive models , volume =

    Philipp Otto and Wolfgang Schmid , doi =. Detection of spatial change points in the mean and covariances of multivariate simultaneous autoregressive models , volume =. Biometrical Journal , keywords =

    work page

  72. [72]

    Control charts for multivariate spatial autoregressive models , volume =

    Robert Garthoff and Philipp Otto , doi =. Control charts for multivariate spatial autoregressive models , volume =. AStA Advances in Statistical Analysis , keywords =

    work page

  73. [73]

    Computing the minimum covariance determinant estimator (MCD) by simulated annealing , volume =

    Valentin Todorov , doi =. Computing the minimum covariance determinant estimator (MCD) by simulated annealing , volume =. Computational Statistics and Data Analysis , keywords =

    work page

  74. [74]

    Hawkins , doi =

    Douglas M. Hawkins , doi =. The feasible solution algorithm for the minimum covariance determinant estimator in multivariate data , volume =. Computational Statistics and Data Analysis , keywords =

    work page

  75. [75]

    Politis , doi =

    Carsten Jentsch and Dimitris N. Politis , doi =. Covariance matrix estimation and linear process bootstrap for multivariate time series of possibly increasing dimension , volume =. The Annals of Statistics , pages =

    work page

  76. [76]

    Heagerty and Thomas Lumley , doi =

    Patrick J. Heagerty and Thomas Lumley , doi =. Window Subsampling of Estimating Functions with Application to Regression Models , volume =. Journal of the American Statistical Association , keywords =

    work page

  77. [77]

    Subsampling a Random Field , volume =

    Antonio Possolo , journal =. Subsampling a Random Field , volume =

    work page

  78. [78]

    Andrew T A Wood and Grace Chan , issue =. Simulation of Stationary Gaussian Processes in [ 0 , 1 ] d Linked references are available on JSTOR for this article : Simulation of Stationary Gaussian Processes in [ 0 , 1 ] d , volume =

    work page

  79. [79]

    On Confidence Intervals for Spatial Parameters Estimated from Nonreplicated Data , volume =

    Peter Hall , issue =. On Confidence Intervals for Spatial Parameters Estimated from Nonreplicated Data , volume =

    work page

  80. [80]

    Simulation and Analysis of Random Fields , volume =

    Martin Schlather , doi =. Simulation and Analysis of Random Fields , volume =. R-News , pages =

    work page

Showing first 80 references.