A class of uniform tests for goodness-of-fit of the multivariate $$L_p$$ L p -norm spherical distributions and the $$l_p$$ l p -norm symmetric distributions

Jiajuan Liang (), Kai Wang Ng and Guoliang Tian
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Jiajuan Liang: University of New Haven
Kai Wang Ng: The University of Hong Kong
Guoliang Tian: Southern University of Science and Technology

Annals of the Institute of Statistical Mathematics, 2019, vol. 71, issue 1, No 6, 137-162

Abstract: Abstract In this paper we employ the conditional probability integral transformation (CPIT) method to transform a d-dimensional sample from two classes of generalized multivariate distributions into a uniform sample in the unit interval $$(0,\,1)$$ ( 0 , 1 ) or in the unit hypercube $$[0,\,1]^{d-1}$$ [ 0 , 1 ] d - 1 ( $$d\ge 2$$ d ≥ 2 ). A class of existing uniform statistics are adopted to test the uniformity of the transformed sample. Monte Carlo studies are carried out to demonstrate the performance of the tests in controlling type I error rates and power against a selected group of alternative distributions. It is concluded that the proposed tests have satisfactory empirical performance and the CPIT method in this paper can serve as a general way to construct goodness-of-fit tests for many generalized multivariate distributions.

Keywords: Goodness-of-fit; Monte Carlo study; $$L_p$$ L p -norm spherical distribution; $$l_p$$ l p -norm symmetric distribution; Uniformity (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10463-017-0630-0

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