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Consider additive functionals of a Markov chain $W_k$, with stationary (marginal) distribution and transition function denoted by $\pi$ and $Q$, say $S_n=g(W_1)+...+g(W_n)$, where $g$ is square integrable and has mean 0 with respect to…

Probability · Mathematics 2008-11-14 Ou Zhao , Michael Woodroofe

We consider a scheme of equiprobable allocation of particles into cells by sets. The Edgeworth type asymptotic expansion in the local central limit theorem for a number of empty cells left after allocation of all sets of particles is…

Probability · Mathematics 2009-05-27 Saidbek S. Mirakhmedov , Sherzod M. Mirakhmedov

A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…

General Relativity and Quantum Cosmology · Physics 2007-05-23 C. Bona , T. Ledvinka , C. Palenzuela , M. Zacek

We use Stein's method to prove a generalization of the Lindeberg-Feller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normally distributed random variable and the rowwise sums of a…

Probability · Mathematics 2011-12-30 Ben Berckmoes , Bob Lowen , Jan Van Casteren

In a landmark contribution to the structural vector autoregression (SVARs) literature, Rubio-Ramirez, Waggoner, and Zha (2010, `Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference,' Review of Economic…

Econometrics · Economics 2026-03-10 Emanuele Bacchiocchi , Toru Kitagawa

The problem of testing two simple hypotheses in a general probability space is considered. For a fixed type-I error probability, the best exponential decay rate of the type-II error probability is investigated. In regular asymptotic cases…

Information Theory · Computer Science 2023-02-27 Marat V. Burnashev

We study the identification of direct and indirect causes on time series and provide conditions in the presence of latent variables, which we prove to be necessary and sufficient under some graph constraints. Our theoretical results and…

Methodology · Statistics 2020-10-23 Atalanti A. Mastakouri , Bernhard Schölkopf , Dominik Janzing

The problem of simultaneous estimation of order restricted location parameters $\theta_1$ and $\theta_2$ ($-\infty<\theta_1\leq \theta_2<\infty$) of a bivariate location symmetric distribution, under a general loss function, is being…

Statistics Theory · Mathematics 2023-09-26 Naresh Garg , Neeraj Misra

We investigate saddlepoint approximations applied to the score test statistic in genome-wide association studies with binary phenotypes. The inaccuracy in the normal approximation of the score test statistic increases with increasing sample…

We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…

Statistics Theory · Mathematics 2013-06-07 Min Tsao , Fan Wu

In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…

Optimization and Control · Mathematics 2022-11-24 Matus Benko , Helmut Gfrerer , Jane Ye , Jin Zhang , Jinchuan Zhou

This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive a generator-based Stein identity from…

Statistics Theory · Mathematics 2026-01-19 Robert E. Gaunt , Frédéric Ouimet , Donald Richards

This paper is concerned with normal approximation under relaxed moment conditions using Stein's method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of…

Probability · Mathematics 2021-06-16 Nguyen Tien Dung

We study the conditional distribution of goodness of fit statistics of the Cram\'{e}r--von Mises type given the complete sufficient statistics in testing for exponential family models. We show that this distribution is close, in large…

Statistics Theory · Mathematics 2012-07-26 Richard A. Lockhart

We derive asymptotic expansions up to order $n^{-1/2}$ for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The…

Statistics Theory · Mathematics 2011-02-23 Artur J. Lemonte , Silvia L. P. Ferrari

A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…

Optimization and Control · Mathematics 2013-10-29 M. Hossein Partovi , Michael R. Caputo

This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and…

Statistics Theory · Mathematics 2012-11-12 Marc Hallin , Davy Paindaveine , Thomas Verdebout

We consider random coefficient autoregressive models of infinite order (AR($\infty$)) under the assumption of non-negativity of the coefficients. We develop novel methods yielding sufficient or necessary conditions for finiteness of…

Probability · Mathematics 2024-09-17 Pascal Maillard , Olivier Wintenberger

We prove an extension of Yuan's Lemma to more than two matrices, as long as the set of matrices has rank at most 2. This is used to generalize the main result of [A. Baccari and A. Trad. On the classical necessary second-order optimality…

Optimization and Control · Mathematics 2017-07-20 Gabriel Haeser

A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…

Dynamical Systems · Mathematics 2015-08-12 Humberto Stein Shiromoto , Vincent Andrieu , Christophe Prieur