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In this paper, we propose a simple inferential method for a wide class of panel data models with a focus on such cases that have both serial correlation and cross-sectional dependence. In order to establish an asymptotic theory to support…

Econometrics · Economics 2023-06-09 Jiti Gao , Bin Peng , Yayi Yan

This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-$P$ version of the weaker Cram\'{e}r condition in Angst…

Statistics Theory · Mathematics 2019-08-14 Kyungchul Song

A large class of statistics can be formulated as smooth functions of sample means of random vectors. In this paper, we propose a general partial Cram\'{e}r's condition (GPCC) and apply it to establish the validity of the Edgeworth expansion…

Probability · Mathematics 2025-11-04 Yashi Wei , Jiang Hu , Zhidong Bai

We derive Edgeworth expansions that describe corrections to the Gaussian limiting behaviour of slow-fast systems. The Edgeworth expansion is achieved using a semi-group formalism for the transfer operator, where a Duhamel-Dyson series is…

Chaotic Dynamics · Physics 2019-02-05 Jeroen Wouters , Georg A. Gottwald

In statistical mechanics, evaluating finite-size macroscopic fluctuations typically relies on Edgeworth expansions. However, these perturbative methods append additive polynomial corrections that inevitably break down in the large deviation…

Information Theory · Computer Science 2026-04-15 Hiroki Suyari

We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…

Machine Learning · Computer Science 2024-10-24 Diego Marcondes , Ulisses Braga-Neto

In this work, we derive an Edgeworth expansion for the Bernoulli weighted mean $\hat{\mu} = \frac{\sum_{i=1}^n Y_i T_i}{\sum_{i=1}^n T_i}$ in the case where $Y_1, \dots, Y_n$ are i.i.d. non semi-lattice random variables and $T_1, \dots,…

Probability · Mathematics 2022-08-22 Pierre-Louis Cauvin

In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain…

Methodology · Statistics 2021-07-14 Ting Ye , Jun Shao , Yanyao Yi , Qingyuan Zhao

In randomized clinical trials, adjusting for baseline covariates can improve credibility and efficiency for demonstrating and quantifying treatment effects. This article studies the augmented inverse propensity weighted (AIPW) estimator,…

Methodology · Statistics 2024-03-27 Marlena S. Bannick , Jun Shao , Jingyi Liu , Yu Du , Yanyao Yi , Ting Ye

The "typical" asymptotic behavior of the weighted sums of independent, identically distibuted random vectors in k-dimensional space is considered. It is shown that under finitnes of fifth absolute moment of an individual term the rate of…

Probability · Mathematics 2023-12-25 Sagak Ayvazyan

Datasets are often reused to perform multiple statistical analyses in an adaptive way, in which each analysis may depend on the outcomes of previous analyses on the same dataset. Standard statistical guarantees do not account for these…

Machine Learning · Computer Science 2017-06-19 Vitaly Feldman , Thomas Steinke

While batching methods have been widely used in simulation and statistics, it is open regarding their higher-order coverage behaviors and whether one variant is better than the others in this regard. We develop techniques to obtain…

Statistics Theory · Mathematics 2021-11-15 Shengyi He , Henry Lam

A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of…

Statistics Theory · Mathematics 2013-12-12 Ibrahim Bin Mohamed , Sherzod M. Mirakhmedov

In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an…

Probability · Mathematics 2019-06-21 Marie Ernst , Gesine Reinert , Yvik Swan

We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several…

Methodology · Statistics 2013-08-16 Tiago M. Vargas , Silvia L. P. Ferrari , Artur J. Lemonte

Testing equality of mean vectors is a very commonly used criterion when comparing two multivariate random variables. Traditional tests such as Hotelling's T-squared become either unusable or output small power when the number of variables…

Methodology · Statistics 2020-03-17 Santu Ghosh , Deepak Nag Ayyala , Rafael Hellebuyck

Outcome-dependent sampling designs are extensively utilized in various scientific disciplines, including epidemiology, ecology, and economics, with retrospective case-control studies being specific examples of such designs. Additionally, if…

Methodology · Statistics 2023-09-22 Min Zeng , Zeyang Jia , Zijian Sui , Jinfeng Xu , Hong Zhang

We propose the family of generalized resubstitution classifier error estimators based on empirical measures. These error estimators are computationally efficient and do not require re-training of classifiers. The plain resubstitution error…

Machine Learning · Statistics 2021-10-26 Parisa Ghane , Ulisses Braga-Neto

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…

Statistics Theory · Mathematics 2023-01-18 Martin Genzel , Christian Kipp

We obtain non-uniform Edgeworth expansions for several classes of weakly dependent (non-stationary) sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or…

Probability · Mathematics 2025-11-11 Yeor Hafouta