Related papers: Approximation by normal distribution for a sample …

In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…

By the Lindeberg-L\'evy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual…

Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…

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…

We apply Lindeberg's method, invented to prove a central limit theorem, to analyze the moderate deviations around such a central limit theorem. In particular, we will show moderate deviation principles for martingales as well as for random…

In this paper, we establish Berry--Esseen bounds for both self-normalized and non-self-normalized sums of locally dependent random variables. The proofs are based on Stein's method together with a concentration inequality approach. We…

In observational studies with time-to-event outcomes, the g-formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

We deduce the non-asymptotical bilateral estimates for moment inequalities for sums of non-negative independent random variables, based on the correspondent estimates for the so-called Bell functions and the Poisson distribution.

Let \{X_1, X_2, ...\} be a sequence of independent and identically distributed positive random variables of Pareto-type with index \alpha>0 and let \{N(t); t\geq 0\} be a counting process independent of the X_i's. For any fixed t\geq 0,…

Central limit theorems for the log-volume of a class of random convex bodies in $\mathbb{R}^n$ are obtained in the high-dimensional regime, that is, as $n\to\infty$. In particular, the case of random simplices pinned at the origin and…

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…

Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…

In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the important Frechet bounds the dependence structure…

In [8], asymptotic expansion of the martingale with mixed normal limit was provided. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard…

Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not…

In this work we prove an asymptotic result, that under some conditions on the involved distribution functions, is valid for any Oppenheim expansion, extending a classical result proven by W. Vervaat in 1972 for denominators of the Luroth…

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…

In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…