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The Product-Moment Correlation Coefficient and Linear Regression for Truncated Data

Chen-Hsin Chen, Wei-Yann Tsai and Wei-Hsiung Chao
Journal of the American Statistical Association
Vol. 91, No. 435 (Sep., 1996), pp. 1181-1186
DOI: 10.2307/2291736
Stable URL: http://www.jstor.org/stable/2291736
Page Count: 6
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The Product-Moment Correlation Coefficient and Linear Regression for Truncated Data
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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.

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