Abstract
The estimation of a biased density for exponentially strongly mixing sequences is investigated. We construct a new adaptive wavelet estimator based on a hard thresholding rule. We determine a sharp upper bound of the associated mean integrated square error for a wide class of functions.
Highlights
In the standard density estimation problem, we observe n random variables X1, . . . , Xn with common density function f
We focus our attention on the wavelet methods because they provide a coherent set of procedures that are spatially adaptive and near optimal over a wide range of function spaces
We develop two new wavelet estimators: a linear nonadaptive based on projections and a nonlinear adaptive using the hard thresholding rule introduced by 15
Summary
In the standard density estimation problem, we observe n random variables X1, . . . , Xn with common density function f. Such a dependence condition arises for a wide class of GARCHtype time series models classically encountered in finance. We develop two new wavelet estimators: a linear nonadaptive based on projections and a nonlinear adaptive using the hard thresholding rule introduced by 15.
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