Estimator Campuran Spline Truncated dan Deret Fourier dalam Regresi Nonparametrik Untuk Data Kategori

Abstract

Nonparametric regression analysis is ideal when data patterns are uncertain because the approach is highly flexible. In some nonparametric cases, each predictor variable exhibits a different form of association with the response variable. Using only one estimator may result in estimates that do not align with the actual data patterns. Therefore, a mixed estimator approach is needed to overcome this problem. This research introduces a truncated spline and Fourier series mixed estimator, in which the relational structure between the response and predictor variables changes across certain intervals, while others demonstrate a recurring pattern. However, most studies on nonparametric regression still use response variables expressed as quantitative data, even though there are conditions where the response variables are categorical data. Therefore, this study will develop a mixed estimator for categorical data. This study aims to obtain truncated spline and Fourier series mixed estimators in nonparametric regression for categorical data using the Maximum Likelihood Estimation method followed by Newton Raphson iteration. This study produces parameter estimators in mixed models by combining truncated spline functions and Fourier series functions in binary categorical data using the Newton Raphson iteration approach.