A Comparative Study of Deconvolution and Direct Kernel Methods for Empirical Bayes Regression Curve Estimation

The possibility of constructing a Bayesian estimator for the regression curve is studied using two different methods: the first is the method of kernel estimation of the prior density in a deconvolution problem, and the second is the method of kernel estimation of the unconditional probability density. The situation when the observed random variable represents the sum of an unknown parameter and a centered normal error with a known variance is considered. Consistent empirical estimators for the regression curve are constructed. A comparison of the empirical counterparts of the regression function showed that the first estimator outperforms the second one for all prior distributions: the mean squared error was 0.008 versus 0.01 in the case of the exponential distribution, 0.002 versus 0.006 for the gamma distribution, and 0.006 versus 0.02 for the mixture distribution.