Multiresponse Nonparametric Regression Model with Mixed Estimator of Truncated Spline and Kernel for Poverty Indicators Analysis in Nusa Tenggara

Regression analysis is a statistical method used to describe the causal relationship between response variables and predictor variables. Regression analysis can be classified into parametric regression, nonparametric regression, and semiparametric regression, depending on whether the regression curve is fully known, unknown, or partially known. This study aims to obtain a multiresponse nonparametric regression model with a mixed spline truncated and kernel estimator. The model obtained is applied to Poverty Indicators in 32 districts/cities in Nusa Tenggara. The response variables include the Percentage of Poor People, Poverty Depth Index, and Poverty Severity Index, while the predictors are the Human Development Index, Open Unemployment Rate, and GRDP per capita. The estimation method used in this research is Weighted Least Square (WLS). The result shows that the Human Development Index predictor variable can be approximated by a truncated spline function, while the Open Unemployment Rate and Gross Regional Domestic Product (GRDP) per capita predictor variables can be approximated by a kernel function. The multiresponse nonparametric regression model with a mixture of truncated spline and kernel estimators can be used to model Poverty Indicators in Nusa Tenggara. Results show that the Human Development Index aligns with the spline function, while the other predictors align with the kernel function. The best model is a model with one knot point and two bandwidths where the model produces an R² value of 89.86% based on the smallest GCV value.