On the Modification of M-out-of-N Bootstrap Method for Heavy-Tailed Distributions

Hannah F. Opayinka, Adedayo A. Adepoju


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 (mmoon) and to compare its performance with m-out-of-n bootstrap method (moon). The distribution involved has finite variance. The simulated data sets used was drawn from Singh-Maddala distribution. The methodology involves decomposition of the empirical distribution and sampling only  times with replacement from a sample size , such that  and . 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 ‘mmoon’ bootstrap method is proposed as an alternative method to ‘moon’ bootstrap method. Choosing an estimator of interest, the statistical precision of the bootstrap estimator is measured through bootstrap estimates of: standard error; absolute bias; coefficient of variation and root mean square error. The findings suggest that ‘mmoon’ performs better than moon in moderate and larger samples and it converges faster


Bootstrap; Decomposition; Heavy-tailed distributions; Singh-Maddala distribution.

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