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We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions…

Statistics Theory · Mathematics 2013-12-18 Liudas Giraitis , Hira L. Koul

The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…

Methodology · Statistics 2020-01-01 Ayanendranath Basu , Abhijit Mandal , Nirian Martin , Leandro Pardo

This paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by Good [Biometrica 40 (1953) 237--264]. This new necessary and sufficient condition extends…

Statistics Theory · Mathematics 2009-08-25 Cun-Hui Zhang , Zhiyi Zhang

The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…

Information Theory · Computer Science 2024-05-30 Valentinian Lungu , Ioannis Kontoyiannis

In this document, we make a round up of the theory of asymptotic normality of sums of associated random variables, in a coherent approach in view of further contributions for new researchers in the field. (Version 01)

Methodology · Statistics 2018-11-20 Gane Samb Lo , Harouna Sangaré , Cheikhna Hamallah Ndiaye

Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given…

Classical Analysis and ODEs · Mathematics 2011-01-26 José Luis López , Nico M. Temme

We study the asymptotic properties of the GLS estimator in multivariate regression with heteroskedastic and autocorrelated errors. We derive Wald statistics for linear restrictions and assess their performance. The statistics remains robust…

Econometrics · Economics 2025-03-19 Koichiro Moriya , Akihiko Noda

We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…

Probability · Mathematics 2019-07-10 V. Yu. Korolev , A. K. Gorshenin , A. I. Zeifman

This paper develops a unified framework for asymptotically minimax robust hypothesis testing under distributional uncertainty, applicable to both Bayesian and Neyman--Pearson formulations (Type-I and Type-II). Uncertainty classes based on…

Statistics Theory · Mathematics 2026-02-10 Gökhan Gül

Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood…

Statistics Theory · Mathematics 2007-06-13 Donglin Zeng , Jianwen Cai

The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…

Statistics Theory · Mathematics 2020-09-01 Giulio Prevedello , Ken R. Duffy

In conditional copula models, the copula parameter is deterministically linked to a covariate via the calibration function. The latter is of central interest for inference and is usually estimated nonparametrically. However, when a…

Methodology · Statistics 2014-03-19 Elif F. Acar , Radu V. Craiu , Fang Yao

This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…

Methodology · Statistics 2015-02-20 Ana M. Bianco , Graciela Boente , Isabel M. Rodrigues

In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main…

Number Theory · Mathematics 2024-08-27 Jerzy Grunwald , Grzegorz Serafin

We develop a theory of local asymptotic normality in the quantum domain based on a noncommutative extension of the Lebesgue decomposition. This formulation gives a substantial generalization of the previous paper [Yamagata, Fujiwara, and…

Quantum Physics · Physics 2017-03-23 Akio Fujiwara , Koichi Yamagata

Let $(x_{i}, y_{i})_{i=1,\dots,n}$ denote independent samples from a general mixture distribution $\sum_{c\in\mathcal{C}}\rho_{c}P_{c}^{x}$, and consider the hypothesis class of generalized linear models $\hat{y} = F(\Theta^{\top}x)$. In…

Statistics Theory · Mathematics 2024-07-22 Yatin Dandi , Ludovic Stephan , Florent Krzakala , Bruno Loureiro , Lenka Zdeborová

A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power…

Statistics Theory · Mathematics 2022-08-10 Dan D. Erdmann-Pham , Jonathan Terhorst , Yun S. Song

We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…

Number Theory · Mathematics 2021-08-31 Victor Volfson

We propose a new approach that combines multiple non-parametric likelihood-type components to build a data-driven approximation of the true likelihood function. Our approach is built on empirical likelihood, a non-parametric approximation…

Methodology · Statistics 2017-12-15 Adam Jaeger , Nicole Lazar

In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance…

Probability · Mathematics 2013-07-08 Qinwen Wang , Jack W. Silverstein , Jianfeng Yao