The Product-Moment Correlation Coefficient and Linear Regression for Truncated Data
作者:
Chen-Hsin Chen,
Wei-Yann Tsai,
Wei-Hsiung Chao,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1996)
卷期:
Volume 91,
issue 435
页码: 1181-1186
ISSN:0162-1459
年代: 1996
DOI:10.1080/01621459.1996.10476987
出版商: Taylor & Francis Group
关键词: Least squares;Pearson's correlation coefficient;Quasi-independence;Random truncation;Truncated regression
数据来源: Taylor
摘要:
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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