%0 Journal Article
%T Wavelet-Based Density Estimation in Presence of Additive Noise under Various Dependence Structures
%A N. Hosseinioun
%J Advances in Pure Mathematics
%P 7-15
%@ 2160-0384
%D 2016
%I Scientific Research Publishing
%R 10.4236/apm.2016.61002
%X We study the following model: <img alt=\"\" src=\"Edit_506a0f8a-bb1c-4469-8604-9b054582c2a2.jpg\" />. The aim is to estimate the distribution of <em>X</em> when only <img alt=\"\" src=\"Edit_4cc82eba-be3e-4d9a-9eb7-59c82c157676.jpg\" />&nbsp;are observed. In the classical model, the distribution of <img alt=\"\" src=\"Edit_29a52c10-66b2-4076-a7f0-19c6cee18b33.bmp\" />&nbsp;is assumed to be known, and this is often considered as an important drawback of this simple model. Indeed, in most practical applications, the distribution of the errors cannot be perfectly known. In this paper, the author will construct wavelet estimators and analyze their asymptotic mean integrated squared error for additive noise models under certain dependent conditions, the strong mixing case, the <em>¦Â</em>-mixing case and the <em>¦Ñ</em>-mixing case. Under mild conditions on the family of wavelets, the estimator is shown to be <img alt=\"\" src=\"Edit_25fde5b8-452f-45d6-9fc9-c1023ee567dd.jpg\" />-consistent and fast rates of convergence have been established.
%K Additive Noise
%K Density Estimation
%K Dependent Sequence
%K Rate of Convergence
%K Wavelet
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=62839