Deconvolution estimators for invariant densities of stationary processes: Method and Simulation

Tóm tắt

In this paper, the authors estimate the invariant density function of a stationary process from noisy observed data, using the kernel density estimation technique. We examine observations that have been contaminated by another stationary process with a known invariant density function. The study focuses on stationary processes with strong mixing properties. Both the ordinary smooth and the supersmooth noise density function classes are investigated. The research establishes upper bounds for the mean squared error of the estimator to evaluate the rate of convergence. The theoretical properties of the estimator's convergence are illustrated through simulation studies, in which the authors estimate invariant density functions for two stationary processes from noisy observed data generated using the R language. Additionally, a computational example with data on Duchenne muscular dystrophy is also presented to demonstrate the estimator's effectiveness.