Abstract
In this paper, we consider the density estimation problem from independent and identically distributed (i.i.d.) biased observations. We develop an adaptive wavelet hard thresholding rule and evaluate its performance by considering risk over Sobolev balls. We prove that our estimation attains a sharp rate of convergence and show the optimality. MSC:49K40, 90C29, 90C31.
Highlights
1 Introduction In practice, it usually happens that drawing a direct sample from a random variable X is impossible
We consider the problem of estimating the density functions f X(x) without observing directly the i.i.d. sample X, X, . . . , Xn
The purpose of this paper is to estimate the density function f X(x) from the samples Y, Y, . . . , Yn. Several examples of this biased data can be found in the literature
Summary
It usually happens that drawing a direct sample from a random variable X is impossible. We consider the problem of estimating the density functions f X(x) without observing directly the i.i.d. sample X , X , . Yn from biased data with the following density function: f g(x)f The purpose of this paper is to estimate the density function f X(x) from the samples Y , Y , .
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