Penalized contrast estimator for adaptive density deconvolution

Penalized contrast estimator for adaptive density deconvolution

The authors consider the problem of estimating the density g of independent and identically distributed variables Xi, from a sample Z1, . . . , Zn where Zi = Xi + σεi, i = 1, . . . , n, ε is a noise independent of X, with σε having known distribution. They present a model selection procedure allowing to construct an adaptive estimator of g and to find non-asymptotic bounds for its L2(R)-risk. T...

Penalized projection estimator for volatility density

We consider the problem of estimating the stationary density of the process Vt in the stochastic volatility model dYt = √ VtdWt whereWt is a standard Brownian motion and Vt a Markov stationary mixing process. We propose a nonparametric adaptive strategy for which we give non asymptotic risk bounds. We discuss the resulting rate and show that it is quite good in some classical examples of volati...

Adaptive Wavelet Estimator for Nonparametricdensity Deconvolution

Hence the problem of estimating g in (1.2) is called a deconvolution problem. The problem arises in many applications [see, e.g., Desouza (1991), Louis (1991), Zhang (1992)] and, therefore, it was studied extensively in the last decade. The most popular approach to the problem was to estimate p x by a kernel estimator and then solve equation (1.2) using a Fourier transform [see Carroll and Hall...

Adaptive paraunitary filter banks for contrast-based multichannel blind deconvolution

In this paper, we present novel algorithms for multichannel blind deconvolution under output whitening constraints. The algorithms are inspired by recently-developed procedures for gradient adaptive paraunitary filter banks. Several algorithms are developed, including one algorithm that successfully deconvolves mixtures of arbitrary non-zero kurtosis source signals. We provide detailed local st...

Gradient Adaptive Algorithms for Contrast-Based Blind Deconvolution