Estimating a Particular Function of the Multiple Correlation Coefficient
研究了在正态分布样本下，用二次损失函数估计多重相关系数参数的问题，发现非线性估计比最佳无偏估计在均方误差上表现更好。
Abstract Let R denote the sample multiple correlation coefficient formed from a sample from a normal distribution with population multiple correlation coefficient . This article considers the problem of estimating the parameter using quadratic loss. The best unbiased estimate of θ is a linear function of Y = R 2/(1 − R 2); it is shown that this is dominated by other linear estimates and that these, in turn, are dominated by nonlinear estimates. A Monte Carlo study indicates that such estimates perform much better than the best unbiased estimate in terms of mean squared error.