Stochastic Processes pp 359-367 | Cite as
A Note on the Consistency of M-Estimates in Linear Models
Chapter
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
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References
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© Springer-Verlag New York, Inc. 1993