TY - JOUR
AU - Cao Xuan Phuong
PY - 2019/01/06
Y2 - 2019/11/21
TI - Estimation of a fold convolution in additive noise model with compactly supported noise density
JF - Science and Technology Development Journal - Natural Sciences
JA - STDJNS
VL - 2
IS - 1
SE - Original Research
DO - https://doi.org/10.32508/stdjns.v2i1.678
UR - http://stdjns.scienceandtechnology.com.vn/index.php/stdjns/article/view/678
AB - 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 .
ER -