Data-Based Adaptive Estimation in an Investment Model

Abstract

We consider improved estimation strategies for the parameters in a capital asset pricing model under a general linear constraint; we suggest candidate subspace, a preliminary test, and shrinkage estimators. We develop a large sample theory for the estimators that include derivation of asymptotic bias and asymptotic distributional risk of the suggested estimators. The asymptotic results demonstrate the superiority of the suggested estimation technique. A simulation study shows that the method suggested here has sound finite sample properties and strongly corroborates with the theoretical result of the article. A data example is also presented to illustrate the suggested estimation strategies.

Keywords:

• Asymptotic bias and risk
• Capital asset pricing model
• Pretest and shrinkage estimator
• Weighted least square estimation

Mathematics Subject Classification:

• 62J05

Acknowledgments

This research was supported by the Natural Sciences and the Engineering Council of Canada. We thank the referee for constructive comments and suggestions, which led to significant improvement in the presentation of this article.