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Marques, Filipe J.; Coelho, Carlos A.

Near-exact distributions for the sphericity likelihood ratio test statistic. (English) Zbl 1138.62033

J. Stat. Plann. Inference 138, No. 3, 726-741 (2008).
Summary: Three near-exact distributions are developed for a sphericity test statistic. The exact probability density function of this statistic is usually represented through the use of the Meijer G function, which renders the computation of quantiles impossible even for a moderately large number of variables. The main purpose of this paper is to obtain near-exact distributions that lie closer to the exact distribution than the asymptotic distributions while, at the same time, correspond to density and cumulative distribution functions practical to use, allowing for an easy determination of quantiles.
In addition to this, two asymptotic distributions that lie closer to the exact distribution than the existing ones were developed. Two measures are considered to evaluate the proximity between the exact and the asymptotic and near-exact distributions developed. As a reference we use the saddlepoint approximations developed by R. W. Butler et al. [Saddlepoint approximations for tests of block independence, sphericity and equal variances and covariances. J. R. Stat. Soc., Ser. B 55, No. 1, 171–183 (1993)] as well as the asymptotic distribution proposed by G. E. P. Box [Biometrika 36, No. 3–4, 317–346 (1949; Zbl 0035.09101)].

Cited in 13 Documents

MSC:

62H15 Hypothesis testing in multivariate analysis
62H10 Multivariate distribution of statistics
62E20 Asymptotic distribution theory in statistics
65C60 Computational problems in statistics (MSC2010)

Keywords:

sphericity test; generalized near-integer gamma distribution; mixtures; characteristic functions; tables

Citations:

Zbl 0035.09101
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Full Text: DOI

References:

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