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A Dimensional CLT for Non‐Central Wilks’ Lambda in Multivariate Analysis

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  • Ronald W. Butler
  • Andrew T. A. Wood

Abstract

. We consider the non‐central distribution of the classical Wilks’ lambda statistic for testing the general linear hypothesis in MANOVA. We prove that as the dimension of the observation vector goes to infinity, Wilks’ lambda obeys a central limit theorem under simple growth conditions on the non‐centrality matrix. In one case we also prove a stronger result: the saddlepoint cumulative distribution function (CDF) approximation for the standardized version of Wilks’ lambda converges uniformly on compact sets to the standard normal CDF. These theoretical results go some way towards explaining why saddlepoint approximations to the distribution of Wilks’ lambda retain excellent accuracy in high‐dimensional cases.

Suggested Citation

  • Ronald W. Butler & Andrew T. A. Wood, 2004. "A Dimensional CLT for Non‐Central Wilks’ Lambda in Multivariate Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 585-601, December.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:4:p:585-601
    DOI: 10.1111/j.1467-9469.2004.00408.x
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