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The assessment of regression models with discrete outcomes is challenging and has many fundamental issues. With discrete outcomes, standard regression model assessment tools such as Pearson and deviance residuals do not follow the…

Methodology · Statistics 2024-01-15 Lu Yang

The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…

Probability · Mathematics 2023-12-22 Philip Broadbridge , Illia Donhauzer , Andriy Olenko

Pearson's chi-squared test, from 1900, is the standard statistical tool for "hypothesis testing on distributions": namely, given samples from an unknown distribution $Q$ that may or may not equal a hypothesis distribution $P$, we want to…

Statistics Theory · Mathematics 2023-10-17 Trung Dang , Walter McKelvie , Paul Valiant , Hongao Wang

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

Methodology · Statistics 2024-04-09 Shijie Cui , Xu Guo , Zhe Zhang

For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…

Machine Learning · Statistics 2021-04-28 Themistoklis P. Sapsis

Reinforcement learning algorithms rely on exploration to discover new behaviors, which is typically achieved by following a stochastic policy. In continuous control tasks, policies with a Gaussian distribution have been widely adopted.…

Machine Learning · Computer Science 2019-03-28 Dmytro Korenkevych , A. Rupam Mahmood , Gautham Vasan , James Bergstra

Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The…

Statistics Theory · Mathematics 2009-06-08 Mahendra Mariadassou , Avner Bar-Hen

This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…

Statistics Theory · Mathematics 2025-10-28 Falong Tan , Xu Guo , Lixing Zhu

This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…

Econometrics · Economics 2025-02-04 Jean-Yves Pitarakis

We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a…

Statistics Theory · Mathematics 2007-06-13 P. M. Robinson

Estimating the empirical distribution of a scalar-valued data set is a basic and fundamental task. In this paper, we tackle the problem of estimating an empirical distribution in a setting with two challenging features. First, the algorithm…

Machine Learning · Computer Science 2023-01-16 Princewill Okoroafor , Vaishnavi Gupta , Robert Kleinberg , Eleanor Goh

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when…

Econometrics · Economics 2025-04-08 David Van Dijcke

As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…

Computation · Statistics 2026-05-19 Chengpu Wang

A consistent goodness-of-fit test for distributional regression is introduced. The test statistic is based on a process that traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function…

Methodology · Statistics 2025-10-10 Gitte Kremling , Gerhard Dikta

We develop a general method to quantify the uncertainties of parton distribution functions and their physical predictions, with emphasis on incorporating all relevant experimental constraints. The method uses the Hessian formalism to study…

High Energy Physics - Phenomenology · Physics 2008-12-18 J. Pumplin , D. Stump , R. Brock , D. Casey , J. Huston , J. Kalk , H. L. Lai , W. K. Tung

In this paper we consider autoregressive models with conditional autoregressive variance, including the case of homoscedastic AR-models and the case of ARCH models. Our aim is to test the hypothesis of normality for the innovations in a…

Methodology · Statistics 2012-11-07 Natalie Neumeyer , Leonie Selk

We study the distribution of a general class of asymptoticallylinear statistics which are symmetric functions of $N$ independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a…

Statistics Theory · Mathematics 2021-02-09 Friedrich Götze , Mindaugas Bloznelis

In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true…

Optimization and Control · Mathematics 2025-10-27 Zhuangzhuang Jia , Yijie Wang , Roy Dong , Grani A. Hanasusanto

This paper discusses asymptotically distribution free tests for the classical goodness-of-fit hypothesis of an error distribution in nonparametric regression models. These tests are based on the same martingale transform of the residual…

Statistics Theory · Mathematics 2009-09-02 Estate V. Khmaladze , Hira L. Koul

In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…

Methodology · Statistics 2026-03-03 Kiran Prajapat , Sharmishtha Mitra , Debasis Kundu