Essays On Recursive Nonparametric Kernel Estimation Of Regression

In the practice of economics it is common that the data are observed not as a sample of fixed size, but rather as an ongoing sequence of a time series. It could be computationally advantageous if the estimate of the unknown function could be updated for each newly arriving data point. On some occasions, there is also a need to update the existing estimate with the newly realized observations. Kalman filter and Bayesian estimation are the commonly encountered techniques to handle these problems in the paradigm of linear parametric estimation. However, few procedures are available for nonlinear models, especially in the nonparametric setting. This thesis attempts to formulate such an estimator using the recursive version of the Nadaraya-Watson estimator.;The recursive estimator for the conditional mean of a nonparametric regression model with independent observations was thoroughly explored in the late 1970\u27s and early 1980\u27s by authors such as Greblicki and Pawlak (1987). The first chapter of this thesis summarizes the constructs and methods of analysis developed in connection with such estimators for independent observations and briefly demonstrates some of their asymptotic properties under the chosen conditions. However, economic time series are generated as economic agents engage in intertemporal optimization and are usually heterogeneous, correlated and unlikely to be linear. There is an incentive for us to extend the study of this recursive nonparametric regression estimator to the case where the observations are correlated. This investigation forms the content of Chapter Two. In Chapter Three, we propose a recursive version of nonparametric kernel estimator of the derivative of a regression function and establish the conditions to ensure that it is consistent and has an asymptotically normal distribution. In Chapter Four, we show an implementation of the recursive estimator and examine its finite sample properties