Approximating a class of goodness-of-fit test statistics

A class of goodness-of-fit tests is considered. The test statistic of each test in this class is an L2-norm of the difference between the empirical characteristic function associated with a random sample and an estimator of the characteristic function of the population in the null hypothesis. Becaus...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2014-08, Vol.102, p.24-38
Main Authors: Alba Fernández, M.V., Jiménez Gamero, M.D., Castillo Gutiérrez, S.
Format: Article
Language:English
Subjects:
Bootstrap distribution estimator
Consistency
Empirical characteristic function
Goodness-of-fit
Taylor approximation
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Summary:A class of goodness-of-fit tests is considered. The test statistic of each test in this class is an L2-norm of the difference between the empirical characteristic function associated with a random sample and an estimator of the characteristic function of the population in the null hypothesis. Because it is not always possible to give an easily computable analytic expression of the test statistic, a numerical integration formula is given to approximate it. The approximation is built by considering a piecewise quadratic Taylor expansion. The null distribution of the resultant test statistic is consistently estimated by means of a bootstrap estimator. A simulation study is carried out to illustrate the accuracy of the numerical approximation, the goodness of the bootstrap estimator of the null distribution and the power of the test. Applications to real data sets are also provided.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2013.04.025