Comparison of Curve Estimation of the Smoothing Spline Nonparametric Function Path Based on PLS and PWLS In Various Levels of Heteroscedasticity

Abstract

Abstract Linearity assumption that has not been fulfilled in the path analysis should use nonparametric approach. This research uses smoothing spline nonparametric path analysis with generated data where the condition of heteroscedasticity level measured through MAPD statistic will be applied to the data. The conditions are MAPD 0.01 – 0.20; 0.21 – 0.40; 0.41 – 0.60; 0.61 – 0.80; and 0.81 – 1.00. The purpose of this research is to determine the comparison of curve estimation of spline smoothing nonparametric path function on every level of heteroscedasticity category (DM) and without considering the heteroscedasticity (TM). The research results found that relative efficiency value of DM (PWLS) estimator with TM (PLS) that is always more than 1 for every heteroscedasticity level and every observation size. Thus, it was obtained better DM estimator (PWLS approach) comparing to TM (PLS).