Spline Semiparametric Regression Model Estimation on Data with Outliers Using Robust M-Estimation Method

Putri Nilam Cayo

doi:10.22146/jmt.51901

Spline Semiparametric Regression Model Estimation on Data with Outliers Using Robust M-Estimation Method

https://doi.org/10.22146/jmt.51901

Putri Nilam Cayo^(1*)

(1) Universitas Gadjah Mada
(*) Corresponding Author

Abstract

Spline semiparametric regression is a regression model that combines parametric components and nonparametric components in one model where the nonparametric components are approximated by spline regression. The estimation method that is generally used to estimate spline semiparametric regression model is least square method. However, the estimation constructed by this method is sensitive to outliers, causing the estimation of parameter values to be biased and the interpretation of results to be inaccurate. In overcoming this problem, the outliers cannot be eliminated because the outliers can contain important information that cannot be provided by other observations. Therefore, we need an estimation method that is resistantto outliers. It is called robust method.The robust method used in this study is M-estimation method. M-estimation method estimates parameters by minimizing the objective function of the residual. The result shows that M-estimation method produces a smaller GCV (Generalized Cross Validation) value than least square method’s.Thus, the parameter estimators generated by M-estimation method are better than least square method’s. Spline semiparametric regression is a regression model that combines parametric components and nonparametric components in one model where the nonparametric components are approximated by spline regression.The estimation method that is generally used to estimate spline semiparametric regression model is least square method. However, the estimation constructed by this method is sensitive to outliers, causing the estimation of parameter values to be biased and the interpretation of results to be inaccurate. In overcoming this problem, the outliers cannot be eliminated because the outliers can contain important information that cannot be provided by other observations. Therefore, we need an estimation method that is resistantto outliers. It is called robust method.The robust method used in this study is M-estimation method. M-estimation method estimates parameters by minimizing the objective function of the residual. The result shows that M-estimation method produces a smaller GCV (Generalized Cross Validation) value than least square method’s.Thus, the parameter estimators generated by M-estimation method are better than least square method’s. Keywords : M-Estimation, Outlier, Robust, Spline Semiparametric Regression

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DOI: https://doi.org/10.22146/jmt.51901