On the modification of M-out-of-N bootstrap method for heavy-tailed distributions

Abstract

This paper is on the modification of 𝑚-out-of-𝑛 bootstrap method for heavy-tailed distributions such as income distribution. The objective of this paper is to present a modified 𝑚-out-of-𝑛 bootstrap method (𝑚𝑚𝑜𝑛) and compare its performance with the existing m-out-of-n bootstrap method (𝑚𝑜o𝑛). The nature of the upper tail of a distribution is the major reason for the poor performance of classical bootstrap methods even in large samples. The ‘𝑚𝑚𝑜𝑛’ bootstrap method was therefore, proposed as an alternative method to ‘𝑚𝑜𝑛’ bootstrap method. The distribution involved has finite variance. The simulated data sets used was drawn from Singh-Maddala distribution. The methodology involved decomposing the empirical distribution and sampling only n⃛ times with replacement from a sample size n, such that n⃛ →∞ as n→∞, and n⃛/n →0. The performances are judged using standard error; absolute bias; coefficient of variation and root mean square error. The findings showed that ‘𝑚𝑚𝑜𝑛’ performed better than 𝑚𝑜𝑛 in moderate and larger samples and it converged faster