On the Estimation of the Correlation Coefficient from Grouped Data
针对因保密问题无法构建个体主文件的情况，提出两个基于分组均值和总方差的相关系数估计量，证明其渐近正态性，并通过蒙特卡洛模拟显示其均方误差比传统估计量低5%至18%。
Abstract This article proposes two estimators of the correlation coefficient, ρ, when statisticians will not construct a master file on individuals because of confidentiality issues. The approach depends on grouping the data according to the values of one of the variables. Group means and total variance for both variables are required to calculate the estimators. The complete bivariate sample need never be compiled. The estimators are shown to be asymptotically normal. Asymptotic and Monte Carlo results are examined. For 1,000 observations in 10 groups, these results indicate that the ratio of the mean squared error (MSE) for one of the proposed estimators relative to that for the usual estimator of ρ ranges from .82 to .95 as ρ ranges from .9 to .25. The proposed estimators are more efficient than previous estimators for grouped data. Key Words: Correlation coefficientOrdered dataGrouped dataConcomitants of order statisticsAsymptotic normality