Approximating the distributions of x2-type mixtures via matching four cumulants

LIANG YU

Publication

Approximating the distributions of x2-type mixtures via matching four cumulants

LIANG YU

Abstract

Nonparametric goodness-of-fit tests often result in test statistic which can be written as a random variable of chi-square-type mixtures. Zhang (2003) proposed to approximate its distribution using a random variable of form chi-square-type mixtures via matching the first three cumulants. In this thesis, we attempt to improve this approximation via matching the first four cumulants using a random variable of form non-central chi-square mixtures, resulting in the so-called non-central chi-square-approximation. Application of the results to nonparametric goodness-of-fit test based on local polynomial smoother is investigated. Two simulation studies are conducted to compare the non-central chi-square-approximation, the central chi-square-approximation and the normal approximation numerically. The methodologies are illustrated using a real data example.