Finite sample penalization in adaptive density deconvolution
We consider the problem of estimating the density g of identically distributed variables X-i, from a sample Z(1), ... , Z(n), where Z(i) = X-i + sigma epsilon(i), i = 1, ... , n and sigma epsilon(i) is a noise independent of X-i with known density sigma(-1) f(epsilon)(center dot/sigma). We numerically study the adaptive estimators, constructed by a model selection procedure described by Comte et al. [2006, Penalized contrast estimator for density deconvolution, Canadian Journal of Statistics, 37(3)]. We illustrate their properties in various contexts and test their robustness (misspecification of errors, dependency and so on). Comparisons are made with respect to deconvolution kernel estimators. It appears that our estimation algorithm, based on a fast procedure, performs very well in all contexts.
density deconvolution adaptive estimation model selection penalized contrast projection estimator simulation study data driven