Estimating Strictly Increasing Regression Functions

Abstract

The maximum likelihood estimate of a nondecreasing regression function with independent, normal errors has been studied in detail in the literature. However, it is often constant over one or more intervals and for this reason may be unacceptable if the regression function is believed to be strictly increasing. Using simulation techniques, the least squares line, the maximum likelihood estimate, and a weighted average of these two are compared here. In each case considered, the weighted average is strictly increasing with probability near one and has smaller total mean squared error than the maximum likelihood estimator.

Key Words:

• Isotone regression
• Strictly increasing regression
• Stein estimators