On Knots locations for Regression Spline Estimator

AbstractRegression splines is one of the methods that are used to estimate the regression curve non parametrically. One of the most important elements that contribute to the application of the method is to determine the degree of the spline function and the number of knots and their locations Choosing the number of knots and their locations is the main problem in estimating the non parametric regression using regression splines and, when carefully selected, the amount of smoothing in the fitted curve will be in optimal conditions. The research is to shed light on two methods of knots locations; the first method includes place of the knots which represents the data quintile and use one of models selection criteria such as ( Generalized Cross Validation) criterion to select the number of these knots. The other method depends on placing the knots on equal spaces and the use of criterion to select the final locations of knots and its number , A comparison is made between the two methods using one of the errors criteria which is ( Mean Average Absolute Error),depending on the experimental data using the simulation method . Through simulation experiments the method of place knots in equal spaces , is better than the method of placing knots in the form of quintile of data .