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Efficient Quantile Regression Analysis With Missing Observations
Chen, Xuerong1; Wan, Alan T. K.2; Zhou, Yong3,4
AbstractThis article examines the problem of estimation in a quantile regression model when observations are missing at random under independent and nonidentically distributed errors. We consider three approaches of handling this problem based on nonparametric inverse probability weighting, estimating equations projection, and a combination of both. An important distinguishing feature of our methods is their ability to handle missing response and/or partially missing covariates, whereas existing techniques can handle only one or the other, but not both. We prove that our methods yield asymptotically equivalent estimators that achieve the desirable asymptotic properties of unbiasedness, normality, and root n-consistency. Because we do not assume that the errors are identically distributed, our theoretical results are valid under heteroscedasticity, a particularly strong feature of our methods. Under the special case of identical error distributions, all of our proposed estimators achieve the semiparametric efficiency bound. To facilitate the practical implementation of these methods, we develop an iterative method based on the majorize/minimize algorithm for computing the quantile regression estimates, and a bootstrap method for computing their variances. Our simulation findings suggest that all three methods have good finite sample properties. We further illustrate these methods by a real data example. Supplementary materials for this article are available online.
KeywordEstimating equations Missing at random Resampling method Semiparametric efficient
Funding ProjectCity University of Hong Kong ; Hong Kong Research Grants Council[CityU - 11302914] ; National Natural Science Foundation of China (NSFC)[71271128] ; National Natural Science Foundation of China[71331006] ; NCMIS ; Shanghai Leading Academic Discipline Project A ; IRTSHUFE
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000357437300021
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Document Type期刊论文
Corresponding AuthorChen, Xuerong
Affiliation1.Georgetown Univ, Biostat & Bioinformat, Washington, DC 20057 USA
2.City Univ Hong Kong, Dept Management Sci, Hong Kong, Hong Kong, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
4.Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai, Peoples R China
Recommended Citation
GB/T 7714
Chen, Xuerong,Wan, Alan T. K.,Zhou, Yong. Efficient Quantile Regression Analysis With Missing Observations[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2015,110(510):723-741.
APA Chen, Xuerong,Wan, Alan T. K.,&Zhou, Yong.(2015).Efficient Quantile Regression Analysis With Missing Observations.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,110(510),723-741.
MLA Chen, Xuerong,et al."Efficient Quantile Regression Analysis With Missing Observations".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 110.510(2015):723-741.
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