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A stepwise algorithm for selecting category boundaries for the chi-squared goodness-of-fit test
Journal article   Peer reviewed

A stepwise algorithm for selecting category boundaries for the chi-squared goodness-of-fit test

Steve M. Bajgier and Lalit K. Aggarwal
Communications in statistics. Theory and methods, v 16(7), pp 2061-2081
01 Jan 1987
DOI: https://doi.org/10.1080/03610928708829490
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Abstract

noncentral chi-square optimal partition
A stepwise algorithm for selecting categories for the chisquared goodness-of-fit test with completely specified continuous null and alternative distributions is described in this paper. The procedure's starting point is an initial partitioning of the sample space into a large number of categories. A second partition with one fewer category is constructed by combining two categories of the original partition. The procedure continues until there are only two categories; the partition in the sequence with the highest estimated power is the one chosen. For illustartive purposes, the performance of the algorithm is evaluated for several hypothesis tests of the from H 0 : normal distribution vs. H 1 : a specific mixed normal distribution. For each test considered, the partition identified by the algorithm was compared to several equiprobable partitions, including the equiprobable partition with the highest estimated power. In all cases but one, the algorithm identified a parttion with higher estimated power than the best equiprobable partition. Applciations of the procedure are discussed.

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Web of Science research areas
Statistics & Probability
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