The Asymptotic Distributions of The Kernel Estimations of The Conditional Mode and Quantiles

Abstract

In this thesis, we study the kernel estimation of the conditional probability density function and two of its aspects, the conditional mode and the conditional quantiles. For the conditional mode, we study the asymptotic normality of its kernel estimation from [18] and we study the conditions under which the conditional mode estimated at flnite distinct points is asymptotically normally distributed. Also, we study the kernel estimation for the conditional quantile from [1] and we study the conditions under which the joint distribution of several conditional quantile is asymptotically normally distributed.