Correlation estimation with singly truncated bivariate data

Correlation coefficient estimates are often attenuated for truncated samples in the sense that the estimates are biased towards zero. Motivated by real data collected in South Sudan, we consider correlation coefficient estimation with singly truncated bivariate data. By considering a linear regression model in which a truncated variable is used as an explanatory variable, a consistent estimator for the regression slope can be obtained from the ordinary least squares method. A consistent estimator of the correlation coefficient is then obtained by multiplying the regression slope estimator by the variance ratio of the two variables. Results from two limited simulation studies confirm the validity and robustness of the proposed method. The proposed method is applied to the South Sudanese children's anthropometric and nutritional data collected by World Vision.