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A class of robust stepwise alternatives to Hotelling's T 2 tests

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  • Govind Mudholkar
  • Deo Kumar Srivastava

Abstract

Hotelling's T 2 test is known to be optimal under multivariate normality and is reasonably validity-robust when the assumption fails. However, some recently introduced robust test procedures have superior power properties and reasonable type I error control with non-normal populations. These, including the tests due to Tiku & Singh (1982), Tiku & Balakrishnan (1988) and Mudholkar & Srivastava (1999b, c), are asymptotically valid but are useful with moderate size samples only if the population dimension is small. A class of B-optimal modifications of the stepwise alternatives to Hotellings T 2 introduced by Mudholkar & Subbaiah (1980) are simple to implement and essentially equivalent to the T 2 test even with small samples. In this paper we construct and study the robust versions of these modified stepwise tests using trimmed means instead of sample means. We use the robust one- and two-sample trimmed- t procedures as in Mudholkar et al. (1991) and propose statistics based on combining them. The results of an extensive Monte Carlo experiment show that the robust alternatives provide excellent type I error control and a substantial gain in power.

Suggested Citation

  • Govind Mudholkar & Deo Kumar Srivastava, 2000. "A class of robust stepwise alternatives to Hotelling's T 2 tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(5), pages 599-619.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:5:p:599-619
    DOI: 10.1080/02664760050076434
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    References listed on IDEAS

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    1. A. C. Bebbington, 1978. "A Method of Bivariate Trimming for Robust Estimation of the Correlation Coefficient," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 221-226, November.
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