Convergence Rates for the Bootstrapped Product-Limit Process

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...

Convergence rates for the central limit theorem.

Sharp Convergence Rates for Nonlinear Product Formulas

Nonlinear versions of the Lie-Trotter product formula exp[t(A + B)] = \im„^x[exp((t/n)A)exp((t/n)B)}" and related formulas are given in this paper. The convergence rates are optimal. The results are applicable to some nonlinear partial differential equations. 0. Introduction. The Lie-Trotter product formula states that (0.1) exp(^)exp(^)exp(^C e,(A + B+c) asn^oo. (The exponent n indicates itera...

A note on the bootstrapped empirical process

Let Fn denote the empirical distribution of a sample of size n from a distribution function F , and let Hn; t denote the distribution of √ n(Fn(t) − F(t)). Contrary to the intuition, Hn; t is not approximated uniformly over t by its bootstrapped counterpart. The main problem is at the values of t near the tails of F . Two results exploring this phenomenon are presented here. c © 2003 Elsevier B...

Almost Sure Convergence Rates for the Estimation of a Covariance Operator for Negatively Associated Samples

Let {Xn, n >= 1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the se...