On the Reweigted Nadaraya-Watson Estimator of the Conditional Density Function

Abstract

The conditional probability density function plays an important role in statistics. It describes the relationship between two random variables, the dependent variable Y and the independent variable X. In this thesis, we studied the kernel estimation of the conditional density function when it is unknown. Also, we studied the kernel estimation of the regression mean function. Firstly, we have studied the Nadaraya-Watson kernel estimator of the conditional density function. Then to overcome the weakness of it, we studied an improvement kernel estimator of the conditional density function, which is called the Reweigted Nadaraya-Watson estimator. For both two estimators, we have established the following asymptotic properties, consistency, unbiasedness and normality for the kernel estimator of the conditional probability density function and the regression mean function. Also, a theoretical comparisons between the two estimators has been given. On the other hand, we have compared between them using two simulated data. The results of the two comparison have indicated that the Reweigted Nadaraya-Watson estimator is better than the Nadaraya-Watson estimator.