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|Title:||Approximate and asymptotic distributions of chi-squared-type mixtures with applications|
Local polynomial smoothing
Nonparametric goodness-of-fit test
|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|
|Appears in Collections:||Staff Publications|
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