Comparison of generalized cross validation and unbiased risk method for selecting optimal knot in spline truncated

Abstract

Gini ratio is an indicator to measure income inequality. Gini ratio of Indonesia in 2017 is 0.391, still far from Gini ratio target by Bappenas in 2019, that is 0.36. The Gini ratio modeling in this study uses a nonparametric regression approach because the form of the regression curve between the Gini ratio and its predictive variables is unknown. One of the estimators in nonparametric regression is spline truncated. Spline truncated has a knot that adjusts to the local characteristics of a function or data more effectively. The number of knots and their location affect the form of regression curve estimation, so it’s important to obtain optimal knot. There are methods for selecting optimal knots, such as Generalized Cross Validation (GCV) and Unbiased Risk (UBR). This study compares GCV and UBR in selecting optimal knots on Gini Ratio data in Indonesia 2017. The criteria of the best model are based on Mean Squared Error (MSE) and R2 values. From the result, the optimal knot from GCV was a combination of 3-2-2-3 knot with MSE of 0.00085 and R2 of 79.18%. Meanwhile, by using UBR, the optimal knot is three knots with MSE of 0.00095 and R2 of 66.42%. In conclusion, GCV generated better model than UBR.