The Effect of the Outliers and Leverage Points in the Construction of the Bayesian and Bootstrap Confidence Intervals

Abstract

The aim of this research is to compare the bootstrap confidence intervals with the Bayesian confidence intervals for smoothing splines as well as the traditional confidence intervals to determine which of these limits are best in the presence of Outliers and Leverage points in data. The simulation experiments were conducted on two models: the first was linear in the presence of data that was contaminated with outliers and the other with the Leverage points: The second model was nonlinear in the presence of data contaminated with outlying observations Simulation experiments were carried out on different samples. The Penalized Least Squares method was used to fit the Nonparametric regression. The Generalized Cross Validation function (GCV) was used to select the amount of smoothing.

Keywords

• outliers
• leverage points
• penalized least squares
• bayesian confidence intervals
• bootstrap confidence intervals
• traditional confidence intervals