Estimation of Quantile Nonparametric Regression Model with Linear Penalized Spline

Nonparametric regression is one method that is flexible and is used when data plots do not follow parametric patterns. Another problem that is often found in real data is outliers in data. One regression method that has been developed by several researchers to overcome data that contains outliers is quantile regression. The advantage of quantile regression is flexibility in modeling data with the heterogeneous conditional distribution. This is very useful in modeling vulnerable data containing outliers. The use of nonparametric regression has also been developed in the quantile regression model because of the flexibility of the regression. In this article, we chose the penalized spline estimator in estimating the nonparametric quantile regression model. The penalized spline is an estimator in a spline that uses knots and smoothing parameters simultaneously, which can analyze irregularly patterned data with more efficient estimated curve results. In this study using penalized quantile spline with the estimation method used is the least absolute deviation.