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

L. C. Zhao, C. Radhakrishna Rao and X. R. Chen
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L. C. Zhao: Pennsylvania State University, Center for Multivariate Analysis
C. Radhakrishna Rao: Pennsylvania State University, Center for Multivariate Analysis
X. R. Chen: Academia Sinica, Graduate School

A chapter in Stochastic Processes, 1993, pp 359-367 from Springer

Abstract: 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

Keywords: Convex Function; Regression Parameter; Design Matrix; Robust Regression; Important Special Case (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1007/978-1-4615-7909-0_41

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