Науковий семінар кафедри теорії ймовірностей, статистики та актуарної математики
Керівники: Ю.С. Мішура
Місце проведення: Корпус мехмату КНУ
Дата: Вт, 22 жовтня 2013
Доповідач: Kairat Mynbaev (International School of Economics, Kazakh-British Technical University, Almaty, Kazakhstan)
Тема: Asymptotic distribution of the Carroll-Delaigle-Hall estimator in measurement error models
Анотація: This presentation is based on joint work with Carlos Martins Filho. Carroll, Delaigle and Hall (2009) considered the problem of nonparametric prediction of a random variable Y based on an explanatory variable X. The problem in their model is complicated by the fact that there are heterogeneous measurement errors on the observed values of X used in estimation and prediction. In this context, they have proposed a new estimator and obtained its consistency. We provide two new results for their estimator. First, we obtained consistency under less restrictive conditions. Specifically, the characteristic function of the underlying kernel does not have to have compact support, higher-order restrictions can be avoided and fractional smoothness of the involved densities is allowed. This is achieved by applying the kernel estimator proposed by Mynbaev & Martins Filho in 2010. Second, we obtain the asymptotic normality of their estimator under the assumption that there are only two types of measurement errors on the observed values of X. Our proof focuses on the case where measurement errors are super-smooth and we use it to discuss other possibilities. The results of a Monte Carlo simulation are provided.