Wavelet linear density estimator for a discrete-time stochastic process: Lp-losses

Frédérique Leblanc

Statistics & Probability Letters, 1996, vol. 27, issue 1, 71-84

Abstract: We establish that the Lp'-loss (2 [less-than-or-equals, slant] p' > [infinity]) of the linear wavelet density estimator for a stochastic process converges at the rate N[-s'/(2s' + 1)] (s' = 1 - 1/p + 1/p') when the density f belongs to the Besov space Bp,qs. This estimator is optimal when p' = p. We suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quadratic characteristic. After a discussion about the assumptions of the main result, we present some examples of Markov processes which satisfy these assumptions.

Keywords: Wavelet; density; estimation; Besov; space; Mixing; sequences; Markov; chains (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (3)

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