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Asymptotic distributions for testing dimensionality in q-based pHd

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  • Cook, R. Dennis
  • Yin, Xiangrong

Abstract

We show that the test statistic for dimension in q-based principal Hessian directions (pHd) is distributed as a linear combination of [chi]2 random variables. Simpler distributions can result depending on the distribution of the predictors and the adequacy of the quadratic model.

Suggested Citation

  • Cook, R. Dennis & Yin, Xiangrong, 2002. "Asymptotic distributions for testing dimensionality in q-based pHd," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 233-243, July.
  • Handle: RePEc:eee:stapro:v:58:y:2002:i:3:p:233-243
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    References listed on IDEAS

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    1. Eaton, M. L. & Tyler, D., 1994. "The Asymptotic Distribution of Singular-Values with Applications to Canonical Correlations and Correspondence Analysis," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 238-264, August.
    2. Bentler, Peter M. & Xie, Jun, 2000. "Corrections to test statistics in principal Hessian directions," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 381-389, May.
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