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.