Improved Estimator of Coefficent of Determination in Multivariate Normal Distribution

Coefficient of determination is an important criterion in different applications. The problem of point estimation of this parameter has been considered by many researchers. In this paper, the class of linear estimators of R^2 was considered. Then, two new estimators were proposed, which have lower risks than other usual estimator, such as the sample coefficient of determination and its adjusted form. Also on the basis of some simulations, we show that the Jacknife estimator is an efficient estimator with lower risk, when the number of observations is small.