Pith. sign in

REVIEW 2 minor 31 references

kNN estimation in semi-functional partial linear regression with missing responses at random

T0 review · 0 major / 2 minor · reviewed 2026-06-26 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Three kNN estimators are introduced for the linear coefficient and nonparametric operator in a semi-functional partial linear model when responses are missing at random.

desk verdict This paper supplies the first asymptotic results for three kNN estimators in a semi-functional partial linear model with MAR missing responses. read the letter →

arxiv 2606.20930 v1 pith:APKTXYW4 submitted 2026-06-18 stat.ME math.STstat.TH

Germán Aneiros , Silvia Novo This is my paper · ORCID
classification stat.MEmath.STstat.TH
keywords kNNestimationpartiallinearregressionfunctionaldatamissingatrandomsemi-functionalmodelasymptoticpropertiesnonparametric
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper addresses estimation in a regression setup that mixes a vector covariate acting linearly with a functional covariate acting nonparametrically, where the scalar response is observed only with probability that depends on the covariates. It constructs three separate kNN procedures that target the finite-dimensional parameter and the infinite-dimensional operator, then derives initial asymptotic properties for these estimators. A reader would care because many real datasets combine low-dimensional measurements with curve or image data and suffer from incomplete responses, so practical methods that respect both features are needed.

What carries the argument

kNN estimators adapted to the semi-functional partial linear structure, using nearest-neighbor averaging in the functional metric to handle the nonparametric component while isolating the linear effect of the vector covariate.

What would settle it

Simulate data exactly from the partial linear model with known beta and m, impose the missing-at-random mechanism, apply the three kNN estimators, and check whether their empirical convergence rates match the paper's stated asymptotic orders.

Watch

Extended reading notes

Core claim

In the model Y = X^T beta + m(X) + epsilon with P(response observed | X, X) = p(X, X) > 0, three kNN-based estimators are proposed: one for beta that uses local averaging after nonparametric adjustment, one for the operator m that averages over nearest neighbors in the functional space, and a combined procedure; first asymptotic results establish consistency or rates for these estimators under the stated missing-at-random mechanism.

Load-bearing premise

The data truly follow a partial linear structure with exactly one linear vector effect and one nonparametric functional effect, and the probability of observing the response depends only on the observed covariates.

Editorial extensions

If this is right

  • The estimators remain well-defined and can be computed when only a subset of responses is observed.
  • Asymptotic results supply rates that separate the linear and functional contributions.
  • The same kNN machinery targets both the finite-dimensional beta and the operator m simultaneously.
  • The approach covers the case where the functional covariate lives in an infinite-dimensional space.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the functional metric used for nearest neighbors is misspecified, the rates for the nonparametric part would degrade while the linear part might remain consistent.
  • The estimators could be paired with cross-validation to choose the number of neighbors without altering the asymptotic claims.
  • Extensions to prediction intervals would require additional variance estimation steps not addressed here.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 2 minor

Summary. The manuscript considers a semi-functional partial linear regression model with scalar response missing at random, a finite-dimensional covariate X with linear effect, and an infinite-dimensional functional covariate Χ with nonparametric effect. Three kNN-based estimators are proposed for the vector parameter and the nonparametric operator, together with initial asymptotic results.

Significance. If the asymptotic results hold under the stated conditions, the work provides practical kNN estimators for mixed-dimensional regression with MAR missingness, extending existing functional data methods. The explicit construction of multiple estimators and the derivation of asymptotics constitute a concrete contribution, though the scope is described as preliminary.

minor comments (2)
  1. [Abstract] Abstract: the description of the three estimators remains high-level; a brief indication of how the kNN weights are combined for the linear and nonparametric components would improve clarity for readers.
  2. The paper should include a short simulation study or real-data illustration to demonstrate finite-sample behavior of the three estimators, as the asymptotics alone leave practical performance unexamined.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their review of our manuscript on kNN estimation in semi-functional partial linear regression with missing responses at random. The report provides a concise summary and recommends minor revision, but lists no specific major comments.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity

full rationale

The paper proposes three kNN-based estimators for the finite-dimensional parameter and the nonparametric operator in a semi-functional partial linear model with MAR missing responses, together with initial asymptotic results. The abstract and description provide no derivation chain, no equations reducing a result to a fitted input by construction, and no load-bearing self-citations or ansatzes. Standard kNN estimation in this setting is externally grounded in nonparametric statistics without evidence of self-referential reduction.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

Review based on abstract only; ledger entries are inferred at the level of standard modeling assumptions rather than explicit paper content.

free parameters (1)
  • k (number of neighbors)
    Choice of k in kNN is typically data-driven or fixed; not specified in abstract.
assumptions (2)
  • domain assumption Missing at random (MAR) mechanism for responses
    Standard assumption invoked for missing-data models; location: abstract.
  • domain assumption Partial linear structure with one linear vector effect and one nonparametric functional effect
    Core model specification; location: abstract.

how reviews work

0 comments
Cite this review

Pith. "Pith review of kNN estimation in semi-functional partial linear regression with missing responses at random." pith.science (2026). https://pith.science/paper/APKTXYW4

@misc{pith2026260620930,
  author       = {Pith},
  title        = {Pith review of: kNN estimation in semi-functional partial linear regression with missing responses at random},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/APKTXYW4}},
  note         = {Machine review of arXiv:2606.20930}
}
abstract

This paper considers a partial linear regression model with scalar response missing at random, one finite-dimensional covariate (a vector, $X$) and one infinite-dimensional covariate (a functional variable, $\mathcal{X}$). While the effect of $X$ on the response is linear, the effect of $\mathcal{X}$ is nonparametric. Three $k$NN-based estimators are proposed for both the vector parameter and the nonparametric operator, and some first asymptotic results are obtained.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

31 extracted references

  1. [1]

    Statistics 49:1322--1347

    Aneiros G, Ferraty F, Vieu P (2015) Variable selection in partial linear regression with functional covariate. Statistics 49:1322--1347

    2015

  2. [2]

    J Multivariate Anal 189:104861

    Aneiros G, Horová I, Hušková M, Vieu P (2022) On functional data analysis and related topics. J Multivariate Anal 189:104861

    2022

  3. [3]

    Statist Probab Lett 76:1102--1110

    Aneiros-Pérez G, Vieu P (2006) Semi-functional partial linear regression. Statist Probab Lett 76:1102--1110

    2006

  4. [4]

    J Multivariate Anal 99:834--857

    Aneiros-Pérez G, Vieu P (2008) Nonparametric time series prediction: A semi-functional partial linear modeling. J Multivariate Anal 99:834--857

    2008

  5. [5]

    J Multivariate Anal 154:59--84

    Boente G, Vahnovan A (2017) Robust estimators in semi-functional partial linear regression models. J Multivariate Anal 154:59--84

    2017

  6. [6]

    C R Acad Sci Paris 289:245--247

    Collomb G (1979) Estimation de la régression par la méthode des k points les plus proches: propriétés de convergence ponctuelle. C R Acad Sci Paris 289:245--247

    1979

  7. [7]

    J Statist Plann Inference 201:103--119

    Crambes C, Henchiri Y (2018) Regression imputation in the functional linear model with missing values in the response. J Statist Plann Inference 201:103--119

    2018

  8. [8]

    Statist Probab Lett 142:92--101

    Ding H, Lu Z, Zhang J, Zhang R (2018) Semi-functional partial linear quantile regression. Statist Probab Lett 142:92--101

    2018

Show all 31 references
  1. [9]

    Comput Statist Data Anal 131:91--103

    Febrero-Bande M, Galeano P, González-Manteiga W (2019) Estimation, imputation and prediction for the functional linear model with scalar response with responses missing at random. Comput Statist Data Anal 131:91--103

    2019

  2. [10]

    Springer, New York

    Ferraty F, Vieu P (2006) Nonparametric Functional Data Analysis: Theory and practice. Springer, New York

    2006

  3. [11]

    Statistics 47:688--706

    Ferraty F, Sued M, Vieu P (2013) Mean estimation with data missing at random for functional covariables. Statistics 47:688--706

    2013

  4. [12]

    Springer

    Horváth L, Kokoszka P (2012) Inference for Functional Data with Applications. Springer

    2012

  5. [13]

    Hsing T, Eubank R (2015) Theoretical Foundations of Functional Data Analysis, With an Introduction to Linear Operators. Wiley

    2015

  6. [14]

    J Multivariate Anal 153:176--188

    Kara-Zaitri L, Laksaci A, Rachdi M, Vieu P (2017) Data-driven kNN estimation in nonparametric functional data analysis. J Multivariate Anal 153:176--188

    2017

  7. [15]

    Special issue on functional data analysis

    Kokoszka P, Oja H, Park B, Sangalli L (2017). Special issue on functional data analysis. Econom Stat 1: 99--100

    2017

  8. [16]

    CRC Press

    Kokoszka P, Reimherr M (2017) Introduction to Functional Data Analysis. CRC Press

    2017

  9. [17]

    Statist Probab Lett 83:1863--1870

    Kudraszow N, Vieu P (2013) Uniform consistency of k NN regressors for functional variables. Statist Probab Lett 83:1863--1870

    2013

  10. [18]

    Metrika 82:39--70

    Ling N, Kan R, Vieu P, Meng S (2019) Semi-functional partially linear regression model with responses missing at random. Metrika 82:39--70

    2019

  11. [19]

    Statist Papers 61:423--444

    Ling N, Aneiros G, Vieu P (2020) kNN estimation in functional partial linear modeling. Statist Papers 61:423--444

    2020

  12. [20]

    Wiley, New York

    Little RJA, Rubin DB (1987) Statistical Analysis with Missing Data. Wiley, New York

    1987

  13. [21]

    J Nonparametr Stat 31:364--392

    Novo S, Aneiros G, Vieu P (2019) Automatic and location-adaptive estimation in functional single-index regression. J Nonparametr Stat 31:364--392

    2019

  14. [22]

    Statistica Neerlandica 75:42--65

    Rachdi M, Laksaci A, Kaid Z, Benchiha A, Al-Awadhi FA (2021) k-Nearest neighbors local linear regression for functional and missing data at random. Statistica Neerlandica 75:42--65

    2021

  15. [23]

    Springer, New York

    Ramsay J, Silverman B (2005) Functional Data Analysis. Springer, New York

    2005

  16. [24]

    Comput Statist 29:829--848

    Shang HL (2014) Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density. Comput Statist 29:829--848

    2014

  17. [25]

    Academic Press, New York

    Stout W (1974) Almost Sure Convergence. Academic Press, New York

    1974

  18. [26]

    Int J Electr Power and Energy Syst 39:48--55

    Vilar JM, Cao R and Aneiros (2012) Forecasting next-day electricity demand and price using nonparametric functional methods. Int J Electr Power and Energy Syst 39:48--55

    2012

  19. [27]

    J Multivariate Anal 211:105491

    Wang T (2026) Robust semi-functional censored regression. J Multivariate Anal 211:105491

    2026

  20. [28]

    J Amer Statist Assoc 99:334--345

    Wang Q, Linton O and Hardle H (2004) Semiparametric regression analysis with missing responses at random. J Amer Statist Assoc 99:334--345

    2004

  21. [29]

    J Multivariate Anal 98:1470--1493

    Wang Q, Sun Z (2007) Estimation in partially linear models with missing responses at random. J Multivariate Anal 98:1470--1493

    2007

  22. [30]

    J Syst Sci Complex 33:1179--1199

    Zhu H, Zhang R, Zhu G (2020) Estimation and inference in semi-functional partially linear measurement error models. J Syst Sci Complex 33:1179--1199

    2020

  23. [31]

    Metrika 82:125--148

    Zhu S, Zhao P (2019) Tests for the linear hypothesis in semi-functional partial linear regression models. Metrika 82:125--148

    2019

Pith tools

Reviewed June 26, 2026 · model on record in the stance chip above.