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Title: L1-optimal estimates for a regression type function in rd
Authors: Yatracos, Yannis G. 
Keywords: Regression analysis;Convergence
Issue Date: 1992
Publisher: Elsevier
Source: Journal of Multivariate Analysis, 1992, Volume 40, Issue 2, Pages 213-220
Abstract: Let X1, X2, ..., Xn be random vectors that take values in a compact set in Rd, d ≥ 1. Let Y1, Y2, ..., Yn be random variables ("the responses") which conditionally on X1 = x1, ..., Xn = xn are independent with densities f(y | xi, θ(xi)), i = 1, ..., n. Assuming that θ lives in a sup-norm compact space Θq,d of real valued functions, an optimal L1-consistent estimator θ ̇n of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θq,d.
ISSN: 0047259X
Rights: © 1992 Elsevier B.V. All rights reserved.
Type: Article
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