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Goodness-of-fit tests for multivariate Laplace distributions. (English) Zbl 1217.62060

Summary: Consistent goodness-of-fit tests are proposed for symmetric and asymmetric multivariate Laplace distributions of arbitrary dimension. The test statistics are formulated following the Fourier-type approach of measuring the weighted discrepancy between the empirical and the theoretical characteristic function, and result in computationally convenient representations. For testing the symmetric Laplace distribution, and in the particular case of a Gaussian weight function, a limit value of these test statistics is obtained when this weight function approaches a Dirac delta function. Interestingly, this limit value is related to a couple of well-known measures of multivariate skewness. A Monte Carlo study is conducted in order to compare the new procedures with standard tests based on the empirical distribution function. A real data application is also included.

MSC:

62G10 Nonparametric hypothesis testing
62H15 Hypothesis testing in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
65C05 Monte Carlo methods

Software:

mvShapiroTest
PDFBibTeX XMLCite
Full Text: DOI

References:

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