Ajit Kumar Majumder

Use of Bootstrapping in Hypothesis Testing: Bootstrapping for Estimation and Hypothesis Testing Ajit Kumar Majumder

The bootstrap is a resampling method for statistical inference, which helps us in most cases, to increase the degree of trust that can be placed in a result based on limited sample of data. When the sample size is small and their EDF is unknown, the bootstrap method is used to make asymptotically normal or near normal. Bootstrap confidence interval thus has double potential advantages over most statistical technique-due to the fact that, it is confidence interval and due to the fact that it is based on bootstrap method. There are several methods of bootstrap confidence interval: the standard method, bootstrap-t, the percentile, the Bias Corrected and Accelerated (BCa) and the approximate bootstrap confidence interval. Among the methods, the BCa method gives us better result with respect to the properties- length, shape and symmetry. ABC method also gives good result in some cases. The bootstrap-t and percentile methods have the identical and close result. The shape of percentile method, in most cases, is good but its forced symmetry makes it poor. In hypothesis testing, bootstrap approach performs better than the classical approach in terms of power.