Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Abstract

Mixed estimators in nonparametric regression have been developed in models with one response. /e biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. /erefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. /is mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. /e mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. /is estimator is also applied to the percentage of the poor population and human development index data. /e results show that the proposed model can be appropriately implemented and gives satisfactory results.