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Title: On the choice of the smoothing parameter for the BHEP goodness-of-fit test
Authors: Tenreiro, Carlos 
Keywords: BHEP goodness-of-fit test; kernel density estimator; Bahadur efficiency; multivariate normality; Monte Carlo power comparison
Issue Date: 2009
Publisher: Elsevier
Project: CMUC/FCT 
Serial title, monograph or event: Computational Statistics and Data Analysis
Volume: 53
Issue: 4
Abstract: The BHEP (Baringhaus--Henze--Epps--Pulley) test for assessing univariate and multivariate normality has shown itself to be a relevant test procedure, recommended in some recent comparative studies. It is well known that the finite sample behaviour of the BHEP goodness-of-fit test strongly depends on the choice of a smoothing parameter $h$. A theoretical and finite sample based description of the role played by the smoothing parameter in the detection of departures from the null hypothesis of normality is given. Additionally, the results of a Monte Carlo study are reported in order to propose an easy-to-use rule for choosing $h$. In the important multivariate case, and contrary to the usual choice of $h$, the BHEP test with the proposed smoothing parameter presents a comparatively good performance against a wide range of alternative distributions. In practice, if no relevant information about the tail of the alternatives is available, the use of this new bandwidth is strongly recommended. Otherwise, new choices of $h$ which are suitable for short tailed and long tailed alternative distributions are also proposed.
DOI: 10.1016/j.csda.2008.09.002
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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