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Probability density estimation from dependent observations using wavelets orthonormal bases. (English) Zbl 0814.62021

Summary: We consider the estimation of the probability density function \(f(x)\) of stationary mixing processes using wavelet orthogonal bases. For \(f\) belonging to the Sobolev space \(H_ 2^ s\), \(s>0\), we derive precise asymptotic expressions for the mean integrated square estimation error.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
46N30 Applications of functional analysis in probability theory and statistics
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