Translator Disclaimer
December, 1989 A Regression Type Problem
Yannis G. Yatracos
Ann. Statist. 17(4): 1597-1607 (December, 1989). DOI: 10.1214/aos/1176347383

Abstract

Let $X_1, \cdots, X_n$ be random vectors that take values in a compact set in $R^d, d = 1, 2$. Let $Y_1, \cdots, Y_n$ be random variables (the responses) which conditionally on $X_1 = x_1, \cdots, X_n = x_n$ are independent with densities $f(y \mid x_i, \theta(x_i)), i = 1, \cdots, n$. Assuming that $\theta$ lies in a sup-norm compact space $\Theta$ of real-valued functions, an $L_1$-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 $\Theta$.

Citation

Download Citation

Yannis G. Yatracos. "A Regression Type Problem." Ann. Statist. 17 (4) 1597 - 1607, December, 1989. https://doi.org/10.1214/aos/1176347383

Information

Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0694.62018
MathSciNet: MR1026301
Digital Object Identifier: 10.1214/aos/1176347383

Subjects:
Primary: 62G05
Secondary: 62G30

Rights: Copyright © 1989 Institute of Mathematical Statistics

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.17 • No. 4 • December, 1989
Back to Top