L1-optimal estimates for a regression type function in Rd

Yannis G. Yatracos

Journal of Multivariate Analysis, 1992, vol. 40, issue 2, 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, [theta](xi)), i = 1, ..., n. Assuming that [theta] lives in a sup-norm compact space [Theta]q,d of real valued functions, an optimal L1-consistent estimator of [theta] is constructed via empirical measures. The rate of convergence of the estimator to the true parameter [theta] depends on Kolmogorov's entropy of [Theta]q,d.

Keywords: minimum; distance; estimation; empirical; measures; nonparametric; regression; rates; of; convergence; Kolmogorov's; entropy; regression; type; function (search for similar items in EconPapers)
Date: 1992
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