On the uniform convergence of deconvolution estimators from repeated measurements

This paper studies the uniform convergence rates of Li and Vuong's (1998, Journal of Multivariate Analysis 65, 139-165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31-46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491-533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.