The Product-Moment Correlation Coefficient and Linear Regression for Truncated Data
针对截断数据，推广了皮尔逊相关系数以衡量两变量在可观测区域的关联，并基于准独立性假设提出新的线性回归估计量，计算简单且可扩展至多元回归。
Abstract The random truncation model has been considered extensively in the literature. Tsai has noted that many previous results hold under the weaker assumption of quasi-independence between the failure time and the truncation time in the observable region of truncated data. We generalize the Pearson product-moment correlation coefficient to measure the association between both time variables in the observable region. We show that if the failure time and the truncation time follow a truncated bivariate normal distribution, then a zero value of the generalized correlation coefficient is equivalent to the quasi-independence. We propose a corresponding sample correlation coefficient and consider its asymptotic behavior. We also study an application of quasi-independence to truncated linear regression with its asymptotic results. The proposed estimator, stemming directly from the least-squares approach, is computationally much simpler and has a natural extension to multiple linear regression. A simulation study shows that the proposed estimator for regression slope competes well with available nonparametric estimators.