Journal Articles - Computer and Information Technology - 2021

Let X, Y ,W, δ and ε be continuous univariate random variables defined on a probability space such that Y = X + ε and W = X + δ. Herein X, δ and ε are assumed to be mutually independent. The variables ε and δ are called classical and Berkson errors, respectively. Their distributions are known exactly. Supposewe only observe a random sample Y1, . . . , Yn from the distribution of Y . This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function FW of W based on the observations as well as on the distributions of ε, δ. An estimator for FW depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, δ and ε, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results.