A refinement of normal approximation to Poisson binomial.
A regeneration proof of the central limit theorem for uniformly ergodic Markov chains.
A remark on the conditioning in limit theorems for dependent random vector in
A Remark on the Strong Law of Large Numbers.
A second order approximation for the inverse of the distribution function of the sample mean
The classical quantile approximation for the sample mean, based on the central limit theorem, has been proved to fail when the sample size is small and we approach the tail of the distribution. In this paper we will develop a second order approximation formula for the quantile which improves the classical one under heavy tails underlying distributions, and performs very accurately in the upper tail of the distribution even for relatively small samples.
A semigroup-theoretic proof of Poisson's limit law.
A semigroup-theoretic proof of the law of large numbers.
A sharp analysis on the asymptotic behavior of the Durbin–Watson statistic for the first-order autoregressive process
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin–Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise....
A survey of limit laws for bootstrapped sums.
A survey on the general central limit problem in Banach spaces
A uniform central limit theorem for dependent variables
Niemiro and Zieliński (2007) have recently obtained uniform asymptotic normality for the Bernoulli scheme. This paper concerns a similar problem. We show the uniform central limit theorem for a sequence of stationary random variables.
A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains.
A universality property for last-passage percolation paths close to the axis.
A Useful Central Limit Theorem for m-Dependent Variables
A version of the Harris-Spitzer "random constant velocity" model for infinite systems of particles
A weak law of large numbers for the sample covariance matrix.
A zero-inflated occupancy distribution: Exact results and Poisson convergence.
About the Lindeberg method for strongly mixing sequences
About the Lindeberg method for strongly mixing sequences
We extend the Lindeberg method for the central limit theorem to strongly mixing sequences. Here we obtain a generalization of the central limit theorem of Doukhan, Massart and Rio to nonstationary strongly mixing triangular arrays. The method also provides estimates of the Lévy distance between the distribution of the normalized sum and the standard normal.
About the stationary states of vortex systems