Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 2, pp. 260--276

A GENERALIZATION OF THE PEARSON'S CHI-SQUARE GOODNESS-OF FIT TEST WITH ESTIMATED CELL FREQUENCIES

By

JIMING JIANG, Case Western Reserve University
P. LAHIRI, University of Nebraska, Lincoln

and

CHIEN-HUA WU, Center for Drug Evaluation, Taiwan

SUMMARY. The paper generalizes the Pearson's chi-square-test to the situation where both the cell frequencies and the cell probabilities involve unknown parameters of the distribution to be tested. The asymptotic null-distribution of the test statistic is shown to follow a weighted chi-square distribution under certain regularity conditions. The proposed test statistic arises very naturally in testing goodness-of-fit of the distributions of random effects in a nested error regression model which has been used extensively in solving a variety of scientific problems in small-area estimation, inference from complex survey data and environmental sciences. For this important special case, the proposed generalized Pearson's test is simplified considerably. The proposed test performs well in a Monte Carlo simulation study. A real life example is considered in which we apply the method to a data set regarding lead contamination of soil.

AMS (1991) subject classification. 62H15.

Key words and phrases. Asymptotic distribution, chi-square-test, Model validation.

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