Bootstrapped Pivots for Sample and Population Means and Distribution Functions

TL;DR

This paper introduces a novel bootstrapped pivot method for constructing confidence intervals for means and distribution functions, achieving smaller errors than traditional approaches.

Contribution

It presents a new bootstrap pivot technique that improves accuracy of confidence intervals for means and distribution functions over classical methods.

Findings

Asymptotic confidence intervals with reduced error

Superior performance compared to traditional t-intervals

Applicable to super-population modeling and distribution estimation

Abstract

In this paper we introduce the concept of bootstrapped pivots for the sample and the population means. This is in contrast to the classical method of constructing bootstrapped confidence intervals for the population mean via estimating the cutoff points via drawing a number of bootstrap sub-samples. We show that this new method leads to constructing asymptotic confidence intervals with significantly smaller error in comparison to both of the traditional t-intervals and the classical bootstrapped confidence intervals. The approach taken in this paper relates naturally to super-population modeling, as well as to estimating empirical and theoretical distributions.