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A Regression Type Problem
Yannis G. Yatracos
The Annals of Statistics
Vol. 17, No. 4 (Dec., 1989), pp. 1597-1607
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2241653
Page Count: 11
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Let X1, ⋯, Xn be random vectors that take values in a compact set in Rd, d = 1, 2. Let Y1, ⋯, 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 lies in a sup-norm compact space Θ of real-valued functions, an L1-consistent estimator (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 Θ.
The Annals of Statistics © 1989 Institute of Mathematical Statistics