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A Note on the Consistency of M-Estimates in Linear Models

In: Stochastic Processes

Author

Listed:
  • L. C. Zhao

    (Pennsylvania State University, Center for Multivariate Analysis
    Academia Sinica, Graduate School)

  • C. Radhakrishna Rao

    (Pennsylvania State University, Center for Multivariate Analysis
    Academia Sinica, Graduate School)

  • X. R. Chen

    (Academia Sinica, Graduate School)

Abstract

Weak consistency of M-estimates of regression parameters in a general linear model is established under the condition $$ {\left( {X_n^{'}{X_n}} \right)^{{ - 1}}} \to 0 $$ as $$ n \to \infty $$ , where X n is the design matrix for the first n observations. The M- estimate is obtained by minimizing the sum of (inline) where ρ is a convex function satisfying some minimal regularity conditions, and ε i is the i-th residual

Suggested Citation

  • L. C. Zhao & C. Radhakrishna Rao & X. R. Chen, 1993. "A Note on the Consistency of M-Estimates in Linear Models," Springer Books, in: Stamatis Cambanis & Jayanta K. Ghosh & Rajeeva L. Karandikar & Pranab K. Sen (ed.), Stochastic Processes, pages 359-367, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-7909-0_41
    DOI: 10.1007/978-1-4615-7909-0_41
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