A Central Limit Theorem with Nonparametric Applications

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

A Martingale Central Limit Theorem

We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given.

Central Limit Theorem Forthe

The Edwards model in one dimension is a transformed path measure for standard Brownian motion discouraging self-intersections. We prove a central limit theorem for the endpoint of the path, extending a law of large numbers proved by Westwater (1984). The scaled variance is characterized in terms of the largest eigenvalue of a one-parameter family of diierential operators, introduced and analyze...

Nonparametric functional central limit theorem for time series regression with application to self-normalized confidence interval

This paper is concerned with the inference of nonparametric mean function in a time series context. The commonly used kernel smoothing estimate is asymptotically normal and the traditional inference procedure then consistently estimates the asymptotic variance function and relies upon normal approximation. Consistent estimation of the asymptotic variance function involves another level of nonpa...

A central limit theorem for functions of a Markov chain with applications to shifts