Semiparametric Biresponse Regression Modeling Mixed Spline Truncated, Fourier Series, and Kernel in Predicting Rainfall and Sunshine

The biresponse semiparametric regression analysis combines parametric and nonparametric components to understand the relationship between two correlated response variables and predictor variables. In this approach, the nonparametric component can be estimated using spline truncated, Fourier series, or kernel methods, each suitable for specific data patterns. This study aims to estimate the parameters of a mixed semiparametric regression model on climate data using the Weighted Least Square (WLS) method and to select optimal knot points, oscillation parameters, and bandwidth based on the smallest Generalized Cross Validation (GCV) value. The results show that the best model combines a spline truncated component with one knot and a Fourier series component with one oscillation, yielding a minimum GCV of 7.401, an R² of 84.66%, and an MSE of 92.33. The findings suggest that the biresponse semiparametric regression model combining spline truncated, Fourier series, and kernel estimators is highly effective for modeling climate data with complex predictor patterns.