A comparison of minimax and least squares estimators in linear regression with polyhedral prior information

✍ Scribed by Karsten Schmidt

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Weight: 460 KB
• Volume: 43
• Category: Article
• ISSN: 0167-8019
• DOI: 10.1007/bf00046993

✦ Synopsis

We consider the linear regression model where prior information in the form of linear inequalities restricts the parameter space to a polyhedron. Since the linear minimax estimator has, in general, to be determined numerically, it was proposed to minimize an upper bound of the maximum risk instead. The resulting so-called quasiminimax estimator can be easily calculated in closed form. Unfortunately, both minimax estimators may violate the prior information. Therefore, we consider projection estimators which are obtained by projecting the estimate in an optional second step. The performance of these estimators is investigated in a Monte Carlo study together with several least squares estimators, including the inequality restricted least squares estimator. It turns out that both the projected and the unprojected quasiminimax estimators have the best average performance.