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On Parameters of Increasing Dimensions

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  • He, Xuming
  • Shao, Qi-Man

Abstract

In statistical analyses the complexity of a chosen model is often related to the size of available data. One important question is whether the asymptotic distribution of the parameter estimates normally derived by taking the sample size to infinity for a fixed number of parameters would remain valid if the number of parameters in the model actually increases with the sample size. A number of authors have addressed this question for the linear models. The component-wise asymptotic normality of the parameter estimate remains valid if the dimension of the parameter space grows more slowly than some root of the sample size. In this paper, we consider M-estimators of general parametric models. Our results apply to not only linear regression but also other estimation problems such as multivariate location and generalized linear models. Examples are given to illustrate the applications in different settings.

Suggested Citation

  • He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
    • Handle: RePEc:eee:jmvana:v:73:y:2000:i:1:p:120-135
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    References listed on IDEAS

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    1. Bai, Z. D. & Wu, Y., 1994. "Limiting Behavior of M-Estimators of Regression Coefficients in High Dimensional Linear Models I. Scale Dependent Case," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 211-239, November.
    2. Bai, Z. D. & Wu, Y., 1994. "Limiting Behavior of M-Estimators of Regression-Coefficients in High Dimensional Linear Models II. Scale-Invariant Case," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 240-251, November.
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