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Abstract

Consider the model Y = X + Z , where Y is an observable random variable, X is an unobservable random variable with unknown density f , and Z is a random noise independent of X . The density g of Z is known exactly and assumed to be compactly supported. We are interested in estimating the m- fold convolution fm=f*...*f on the basis of independent and identically distributed (i.i.d.) observations Y1,..,Yn drawn from the distribution of Y . Based on the observations as well as the ridge-parameter regularization method, we propose an estimator for the function fm depending on two regularization parameters in which a parameter is given and a parameter must be chosen. The proposed estimator is shown to be consistent with respect to the mean integrated squared error under some conditions of the parameters. After that we derive a convergence rate of the estimator under some additional regular assumptions for the density f .



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Article Details

Issue: Vol 2 No 1 (2018)
Page No.: 76-83
Published: Jan 6, 2019
Section: Original Research
DOI: https://doi.org/10.32508/stdjns.v2i1.678

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Creative Commons License

Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 How to Cite
Phuong, C. X. (2019). Estimation of a fold convolution in additive noise model with compactly supported noise density. Science and Technology Development Journal - Natural Sciences, 2(1), 76-83. https://doi.org/https://doi.org/10.32508/stdjns.v2i1.678

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