Comparison between confidence intervals of linear regression models with and without restrication

Abstract

In many applications of regression analysis we are interested in curve fitting with some prior knowledge about the structure. For example, this occurs when the experimenter has a strong belief that the regression function changes monotonically with some or all of the predictor variables in a region of interest. The analyses needed for statistical inferences under such constraints are nonstandard. We have considered the statistical inference of a linear regression model with a monotone constraint in Murkerjee and Tu(1995). A natural question is: “What is the difference between the cases of with and without the constraint?” In this article we compare the width of the confidence intervals of a linear regression model with and without the constraint.

Keywords:

• linear regression
• confidence interval
• parameter restriction