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8.2 Bootstrap Methods Based on Marginal ... > 8.2.5 Percentile Bootstrap Methods - Pg. 392

392 Introduction to Robust Estimation and Hypothesis Testing 8.2.5 Percentile Bootstrap Methods This section describes two types of percentile bootstrap methods that can be used to compare J dependent groups based on any measures of location, , associated with the marginal distributions. Included as special cases are M-measures of location and trimmed means. The goal is to test H 0 : 1 = · · · = J . (8.1) Method RMPB3 The first method uses the test statistic Q = ^ ¯ ( j - ) 2 , ¯ ^ where = j /J . An appropriate critical value is estimated using an approach similar to the ^ bootstrap-t technique. First, set C i j = X i j - j . That is, shift the empirical distributions so that the null hypothesis is true. Next a bootstrap sample is obtained by resampling, with replacement, as described in step 1 of Section 8.2.1. As usual, label the results C 11 , . . . , C 1J