Please use this identifier to cite or link to this item: https://doi.org/10.1198/016214504000000575
Title: Approximate and asymptotic distributions of chi-squared-type mixtures with applications
Authors: Zhang, J.-T. 
Keywords: Chi-squared approximation
Chi-squared-type mixtures
Local polynomial smoothing
Nonparametric goodness-of-fit test
Normal approximation
Orthogonal series
Smoothing splines
Issue Date: Mar-2005
Citation: Zhang, J.-T. (2005-03). Approximate and asymptotic distributions of chi-squared-type mixtures with applications. Journal of the American Statistical Association 100 (469) : 273-285. ScholarBank@NUS Repository. https://doi.org/10.1198/016214504000000575
Abstract: In this article we study how to approximate a random variable T of general chi-squared-type mixtures by a random variable of the form aX d 2+ β matching the first three cumulants. The approximation error bounds for the density functions of the chi-squared approximation and the normal approximation are established. Applications of the results to some nonparametric goodness-of-fit tests, including those tests based on orthogonal series, smoothing splines, and local polynomial smoothers, are investigated. Two simulation studies are conducted to compare the chi-squared approximation and the normal approximation numerically. The chi-squared approximation is illustrated using a real data example for polynomial goodness-of-fit tests. © 2005 American Statistical Association.
Source Title: Journal of the American Statistical Association
URI: http://scholarbank.nus.edu.sg/handle/10635/105008
ISSN: 01621459
DOI: 10.1198/016214504000000575
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