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Alba Fernández, M. V.; Jiménez Gamero, M. D.; Castillo Gutiérrez, S.

Approximating a class of goodness-of-fit test statistics. (English) Zbl 1533.62031

Math. Comput. Simul. 102, 24-38 (2014).
Summary: A class of goodness-of-fit tests is considered. The test statistic of each test in this class is an \(L_2\)-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.

Cited in 1 Document

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62-08 Computational methods for problems pertaining to statistics

Keywords:

empirical characteristic function; goodness-of-fit; Taylor approximation; bootstrap distribution estimator; consistency
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References:

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