Statistica Sinica 15(2005), 1081-1096

CONFIDENCE INTERVALS FOR THE MEAN VALUE OF

RESPONSE FUNCTION IN GENERALIZED

LINEAR MODELS

Jin Xu and Arjun K. Gupta

Bowling Green State University

Abstract: Confidence intervals for the mean value of the response function in generalized linear models are proposed to improve the accuracy of the approximation when the distribution of response is nonnormal and the sample size is moderate. The correction will give the approximation error up to order of $\o(n^{-1/2})$ for the one-sided case and of $\o(n^{-1})$ for the two-sided case. Monte Carlo studies are given to compare our results with the classical ones.

Key words and phrases: Confidence intervals, Edgeworth expansion, Skorohod representation, coverage probability, generalized linear models.