Asymptotic Properties of the Deconvolution Kernel Density Estimate based on 2-Dependent Error Structure with Applications to Remaining Useful Life Problems in Reliability Theory
Abstract
This thesis is motivated from an engineering question, which led us to the deconvolution problem with a dependent error structure. We establish a deconvolution kernel density estimator by adapting the methods of kernel density estimates and Fourier Transforms. In this approach, the contaminated data with additive random errors are assumed dependent and satisfying smooth or super smooth conditions. Under both smooth and supper smooth conditions, we derived:
1. optimal rates of convergence in terms of mean integrated squared error for deconvolution kernel density estimator;
2. the limiting distribution of the estimator.