Rates of convergence for minimal distances in the central limit theorem under projective criteria

Rates of convergence for minimal distances in the central limit theorem under projective criteria

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

Convergence rates for the central limit theorem.

Variations on the Projective Central Limit Theorem

This expository article states and proves four, concrete, projective, central limit theorems. The results are known or suspected to be true by experts who are familiar with the more general central limit theorem for convex bodies, and related theory. Here we consider only four types of high dimensional geometric objects: spheres, balls, cubes, and boundaries of cubes. Each is capable of transfo...

The central limit theorem under random truncation.

Under left truncation, data (X(i), Y(i)) are observed only when Y(i) ≤ X(i). Usually, the distribution function F of the X(i) is the target of interest. In this paper, we study linear functionals ∫ φ dF(n) of the nonparametric maximum likelihood estimator (MLE) of F, the Lynden-Bell estimator F(n). A useful representation of ∫ φ dF(n) is derived which yields asymptotic normality under optimal m...

Strong Convergence Rates of the Product-limit Estimator for Left Truncated and Right Censored Data under Association

Non-parametric estimation of a survival function from left truncated data subject to right censoring has been extensively studied in the literature. It is commonly assumed in such studies that the lifetime variables are a sample of independent and identically distributed random variables from the target population. This assumption is often prone to failure in practical studies. For instance, wh...