Mixed estimators spline truncated, kernel, and Fourier series in nonparametric regression for longitudinal data

Abstract

Nonparametric regression is one of the approaches in regression analysis to determine the relationship pattern between predictor variable and response variable. This approach can be used when the data pattern is unknown. Recently, researchers have assumed that every predictor variable in nonparametric regression has the same data pattern by using one form of the estimator for all predictor variables. However, in many cases, there are different data patterns for the relationship of each predictor variable and response variable that partially change in certain sub-intervals, some do not have a set pattern, and some others have a repeating pattern. If the estimation of each predictor variable only uses one form of an estimator, it will produce a bias estimation. Therefore, it requires a mixed estimator to get the better nonparametric regression estimation which is set with data patterns. This research evolves a mixed Spline Truncated, Kernel, and Fourier Series estimator for nonparametric regression estimation. It was applied to longitudinal data that repeatedly measured in each subject at different time intervals. A real case was presented to estimate the problem of poverty in 34 provinces in Indonesia from 2015 to 2020. Weighted Least Square (WLS) approach was utilized as method of the estimation. Based on the results of the analysis, the best nonparametric regression model was obtained, namely the model with 1 knot 1 oscillation, with the smallest GCV value of 0.25.