Accession Number : ADA308749

Title :   Bootstrap by Sequential Resampling.

Descriptive Note : Technical rept.,

Corporate Author : PENNSYLVANIA STATE UNIV UNIVERSITY PARK CENTER FOR MULTIVARIATE ANALYSIS

Personal Author(s) : Rao, C. R. ; Pathak, P. K. ; Koltchinskii, V. I.

PDF Url : ADA308749

Report Date : FEB 1996

Pagination or Media Count : 27

Abstract : This paper examines methods of resampling for bootstrap from a survey sampling point of view. Given an observed sample of size n resampling for bootstrap involves n repeated trials of simple random sampling with replacement. From the point of view of information content it is well known that simple random sampling with replacement does not result in samples that are equally informative. This is due to different numbers of distinct observations occuring in different bootstrap samples. We propose an alternative scheme of sampling sequentially (with replacement each time) until k distinct original observations appear. In such a scheme the bootstrap sample size becomes random as it varies from sample to sample but each sample has exactly the same number of distinct observations. We show that the choice of k = (1 - e(-1) )n approx. 632n has some advantage, stemming from the observation made by Efron that the usual bootstrap samples are supported on approximately .632n of the original data points. Listing recent results on empirical processes. We show that main empirical characteristics of the sequential resampling bootstrap are asymptotically within the distance of order approx n(-3/4) of the corresponding characteristics of the usual bootstrap.

Descriptors :   *SEQUENTIAL ANALYSIS, *STATISTICAL SAMPLES, PROBABILITY DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, STATISTICAL DATA, APPROXIMATION(MATHEMATICS), CONVERGENCE, HEURISTIC METHODS, STATISTICAL PROCESSES, SEQUENCES(MATHEMATICS), NORMAL DISTRIBUTION, INEQUALITIES.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE