Integral Estimator with Kernel Approach for Estimating Nonparametric Regression Functions

Abstract

Abstract Derivatives are measurements of how a function change as the input value changes, or in general a derivative shows how one quantity changes due to a change in another quantity. The concept of universal or comprehensive function derivatives is widely used in various scientific fields. For example, in economics, people are interested in studying the condition of the derivative of an objective function as the result of an optimization problem. In this study, nonparametric procedures are used to estimate a function where the form of the function does not lead to a particular function model. Suppose we are given a nonparametric regression model where f is an unknown function. The main problem of regression analysis is to determine the form of estimation f. To determine the estimation of f, one approach that can be used is the integral estimator with the Gaussian Kernel approach. Furthermore, as an application, the Labour Force Participation Rate (y) data is used with the predictor variable, namely the Average Length of Schooling (x). By using the GCV (Generalized Cross Validation) method, the optimal bandwidth is obtained at h = 80 with a GCV value of 0.243 with an MSE value of 32.1864.