Laplace deconvolution with dependent errors: a minimax study

Abstract

We investigate minimax results for the anisotropic functional deconvolution model when observations are affected by the presence of long-memory. Under specific conditions about the covariance matrices of the errors, we follow a standard procedure to construct an adaptive wavelet-based estimator that attains asymptotically near-optimal convergence rates. These rates depend on the parameter associated with the weakest long-range dependence, and deteriorate as the intensity of long-memory increases. This behavior suggests that the estimator adjusts to the best case scenario and that the weakest LM dominates.

Estimation in nonparametric regression model with additive and multiplicative noise via Laguerre series

“…Proof of Lemma 4. Below, we use a combination of Lemma 2 in [1], which is an adaptation of Hanson-Wright inequality to matrices, and large deviation result that was developed in [13] and further improved in [17] which states that for any x > 0, if ξ n is a zero mean Gaussian vector with independent elements, and Q is nonnegative definite matrix, then…”

Anisotropic functional deconvolution with long-memory noise: the case of a multi-parameter fractional Wiener sheet

“…One can list; Wang (1996, Wishart (2013), Benhaddou et al (2014) and Kulik et al (2015). In a few other relevant contexts, LM was also investigated in density deconvolution in , and in the Laplace deconvolution in Benhaddou (2018) where the unknown response function f (·) is non-periodic and defined on the entire positive real half-line.…”