Exact composition of mechanisms under multiple simultaneous DP constraints is represented as a mixture of heterogeneous compositions using a structural lemma for binary hypothesis tests.
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Aumann (1976): Agreeing to Disagree
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The Bayes-optimal classifier for elliptical distributions is derived in closed form from the radial generator, yielding a tuning-free alternative to spline GAMs with proven consistency.
A Bayesian predictive model adaptively selects martingale factors to construct asymptotically log-optimal confidence sequences for bounded means while preserving anytime validity under misspecification.
Power-one sequential tests exist for testing any weakly compact null set of distributions against its complement.
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
NOMAD unifies shrinkage and thresholding estimation by minimizing a data-driven approximate risk criterion derived via Stein's identity and Tweedie's formula, recovering James-Stein and lasso as special cases.
A cycle-counting-ratio estimator for the β-model achieves minimax-optimal MSE and consistency under the weak conditions θ_max→0 and θ_t‖θ‖₁→∞, even at network densities near log n/n.
A game-theoretic reformulation of sequential detection shows the LIL as the minimax boundary, with the optimal mixing prior being the Jeffreys prior on the scale-of-scales selected by the Erdős-Kolmogorov test, yielding a 3/2 coefficient for the first iterated-log correction.
Introduces Hellinger distance and negative exponential disparity robust estimators for polychoric correlation under complex surveys, with penalized variants, consistency theory, and simulation comparisons under contamination.
The IM interval is the shortest valid prior-free procedure for the Behrens-Fisher problem, established via cylindrical predictive random sets, minimaxity, admissibility, and a projection argument.
The nonparametric Kiefer-Weiss problem is solved by deriving an optimal stopping policy based on a two-dimensional statistic (likelihood ratio plus expected remaining sample size) whose randomization rule maps the likelihood ratio to an integer sample size.
Empirical plant-animal network data and generalized Lotka-Volterra simulations identify SWAPS interaction distributions as a community signature that requires taxonomic constraints, multiple interaction types, and accompanies elevated diversity and complexity.
Linear-rate ODE hierarchies can be solved in-window exactly—no boundary cap—by integrating a low-dimensional coefficient ODE and composing generating functions; Strang splitting extends the trick to partially linear-rate models like Schlögl and predator-prey.
A functional central limit theorem for pattern frequencies in 2D samples enables nonparametric goodness-of-fit, two-sample, and symmetry tests for copulas, with bootstrap critical values and parametric examples.
A continuous latent seroreactivity model generalizes binary mixture models for antibody data, adds an L2 estimator with consistency proof, and is demonstrated on malaria serology.
Introspection axioms are conservative for agent-alternating formulas in multi-agent belief logics (K/KD) but not in knowledge logics (KT).
Establishes root-n consistency and asymptotic normality for the plug-in estimator of E[F_Y^{-1} ∘ F_Z(X)] under weaker conditions allowing unbounded support, plus a consistent variance estimator.
Adaptive GLM with MQLE and GP regression with UCB for dynamic insurance pricing, showing parameter convergence and regret analysis under delayed claims.
The body of this submission derives (with gaps) a β-mixing U-statistic limit for a spatial Cramér–von Mises test, while the abstract promises a different general-dimensional origin-invariant statistic that never appears in the text.
Consistency among prior, posteriors, and information sets implies information sets form a partition almost surely, posteriors equal Bayes updates, and qualitative beliefs become fully introspective knowledge in standard settings.
A Bayesian reframing of the original Wigner's Friend setup shows compatibility and agreement between observers with no paradoxical conclusion.
A review summarizing definitions, canonical forms, exact and approximate distributions, numerical methods, applications, and open problems for quadratic forms in real and complex Gaussian variables, including multiforms and ratios.
citing papers explorer
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Composition Theorems for Multiple Differential Privacy Constraints
Exact composition of mechanisms under multiple simultaneous DP constraints is represented as a mixture of heterogeneous compositions using a structural lemma for binary hypothesis tests.
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Closed-form fractional radial links for elliptical Mahalanobis discriminant analysis
The Bayes-optimal classifier for elliptical distributions is derived in closed form from the radial generator, yielding a tuning-free alternative to spline GAMs with proven consistency.
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Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means
A Bayesian predictive model adaptively selects martingale factors to construct asymptotically log-optimal confidence sequences for bounded means while preserving anytime validity under misspecification.
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Power one sequential tests exist for weakly compact $\mathscr P$ against $\mathscr P^c$
Power-one sequential tests exist for testing any weakly compact null set of distributions against its complement.
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Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
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Approximate Risk Minimization Over Shrinking-Thresholding Rules in Normal Mean Estimation
NOMAD unifies shrinkage and thresholding estimation by minimizing a data-driven approximate risk criterion derived via Stein's identity and Tweedie's formula, recovering James-Stein and lasso as special cases.
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Subgraph counting estimation for the $\beta$-model in sparse networks
A cycle-counting-ratio estimator for the β-model achieves minimax-optimal MSE and consistency under the weak conditions θ_max→0 and θ_t‖θ‖₁→∞, even at network densities near log n/n.
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The multiply iterated law of the iterated logarithm: game-theoretic foundations of sequential detection boundaries
A game-theoretic reformulation of sequential detection shows the LIL as the minimax boundary, with the optimal mixing prior being the Jeffreys prior on the scale-of-scales selected by the Erdős-Kolmogorov test, yielding a 3/2 coefficient for the first iterated-log correction.
-
Robust Estimation of Polychoric Correlation for Complex Survey Designs Using Minimum Divergence Methods
Introduces Hellinger distance and negative exponential disparity robust estimators for polychoric correlation under complex surveys, with penalized variants, consistency theory, and simulation comparisons under contamination.
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Revisiting the Behrens-Fisher Problem: Validity-First Optimality
The IM interval is the shortest valid prior-free procedure for the Behrens-Fisher problem, established via cylindrical predictive random sets, minimaxity, admissibility, and a projection argument.
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The Nonparametric Kiefer-Weiss Problem
The nonparametric Kiefer-Weiss problem is solved by deriving an optimal stopping policy based on a two-dimensional statistic (likelihood ratio plus expected remaining sample size) whose randomization rule maps the likelihood ratio to an integer sample size.
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Skewed weak and Pareto-tailed strong interactions accompany community diversity and complexity
Empirical plant-animal network data and generalized Lotka-Volterra simulations identify SWAPS interaction distributions as a community signature that requires taxonomic constraints, multiple interaction types, and accompanies elevated diversity and complexity.
-
Operator splitting for exploiting linear-rate closure in solving infinite ODE hierarchies
Linear-rate ODE hierarchies can be solved in-window exactly—no boundary cap—by integrating a low-dimensional coefficient ODE and composing generating functions; Strang splitting extends the trick to partially linear-rate models like Schlögl and predator-prey.
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Pattern-based tests for two-dimensional copulas
A functional central limit theorem for pattern frequencies in 2D samples enables nonparametric goodness-of-fit, two-sample, and symmetry tests for copulas, with bootstrap critical values and parametric examples.
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A flexible class of latent variable models for the analysis of antibody response data
A continuous latent seroreactivity model generalizes binary mixture models for antibody data, adds an L2 estimator with consistency proof, and is demonstrated on malaria serology.
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When Do Introspection Axioms Matter for Multi-Agent Epistemic Reasoning?
Introspection axioms are conservative for agent-alternating formulas in multi-agent belief logics (K/KD) but not in knowledge logics (KT).
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Asymptotic Properties of Empirical Quantile-Based Estimators
Establishes root-n consistency and asymptotic normality for the plug-in estimator of E[F_Y^{-1} ∘ F_Z(X)] under weaker conditions allowing unbounded support, plus a consistent variance estimator.
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Adaptive Pricing in Insurance: Generalized Linear Models and Gaussian Process Regression Approaches
Adaptive GLM with MQLE and GP regression with UCB for dynamic insurance pricing, showing parameter convergence and regret analysis under delayed claims.
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Weak Convergence and Gaussian Limits for a General-Dimensional Origin-Invariant Cram\'er--von Mises Statistic
The body of this submission derives (with gaps) a β-mixing U-statistic limit for a spatial Cramér–von Mises test, while the abstract promises a different general-dimensional origin-invariant statistic that never appears in the text.
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On the Consistency among Prior, Posteriors, and Information Sets (Extended Abstract)
Consistency among prior, posteriors, and information sets implies information sets form a partition almost surely, posteriors equal Bayes updates, and qualitative beliefs become fully introspective knowledge in standard settings.
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Agreement and Compatibility in Wigner's Friend Paradox
A Bayesian reframing of the original Wigner's Friend setup shows compatibility and agreement between observers with no paradoxical conclusion.
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Quadratic Forms in Gaussian Random Variables Theoretical Results and Applications
A review summarizing definitions, canonical forms, exact and approximate distributions, numerical methods, applications, and open problems for quadratic forms in real and complex Gaussian variables, including multiforms and ratios.
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