Abstract
Consider a linear regression model, Y=β' X+ε where Y may be right censored and the cdf F o of ε is unknown. We show that a modified semi-parametric MLE, denoted by \(\hat\beta\) is strongly consistent under certain regularity conditions. Moreover, if F o is discontinuous, then P(\(\hat\beta\)≠β i.o.)=0, which means that P(\(\hat\beta\)=β if the sample size is large)=1. The latter property has not been reported for the existing estimators. By contrast, most estimators, such as the Buckley-James estimator and M-estimators \(\tilde\beta\), satisfy that P(\(\tilde\beta\)≠β i.o.)=1.
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References
Theil H., A rank-invariant method of linear and polynomial regression analysis, I. Proc. Kon. Ned. Akad. v. Wetensch. A, 1950, 53:386–392
Sen P. K., Estimates of the regression coefficient based on Kendall' tau, JASA, 1968, 63:1379–1389
Bickel P. J., On adaptive estimation, Ann. Statist., 1982, 10:647–671
Huber P. J., Robust estimation of a location parameter, Ann. Math. Statist., 1964, 35:73–101
Ritov Y ., Estimation in a linear regression model with censored data, Ann. Statist., 1990, 18:303–328
Montegomery D. C., Peck E. A., Introduction to linear regression analysis, New York:Wiley, 1992
Draper N. R., Smith H., Applied Regression analysis, New York:Wiley, 1981
Zhang C. H., Li X., Linear regression with doubly censored data, Ann. Statist., 1996, 24:2720–2743
Miller R. G., Least squares regression with censored data. Biometrika, 1976, 63:449–464
Buckley J., James I., Linear regression with censored data, Biometrika, 1979, 66:429–436
Chatterjee S., Mcleish D. L., Fitting linear regression models to censored data by least squares and maximum likelihood methods, Comm. Stat. A, 1986, 15:3227–3243
Leurgans S., Linear models, random censoring and synthetic data, Biometrika, 1987, 74:301–309
Hillis S. L., Extending M-estimation to include censored data via James's method, Comm. Stat. B, 1991, 20:121–128
Tsiatis A., A estimating regression parameters using linear rank tests for censored data, Ann. Statist., 1990, 18:354–372
Wei L. J., Ying Z. L., Lin D. Y., Linear regression analysis of censored survival data based on rank tests, Biometrika, 1990, 77:845–851
Akritas M. G., Murphy S. A., Lavalley M. P., The Theil-Sen estimator with doubly censored-data and appli cations to astronomy, JASA, 1995, 90:170–177
Moon C. G., A Monte Carlo comparison of semiparametric Tobit estimators, Journal of Applied Econometics, 1989, 4:361–382
Yu Q. Q., Wong, G. Y. C., The semi-parametric MLE in linear regression analysis with right-censored data, (Submitted for publication)
Yu Q. Q., Schick A., Li L. X., Wong G. Y. C., Asymptotic properties of the GMLE of a survival function with case 2 interval-censored data, Statist. & Prob. Let., 1998, 37:223–228
Groeneboom P., Wellner J. A., Information bounds and nonparametric maximum likelihood estimation, Basel: Birkhäuser Verlag, 1992
Yu Q. Q., Wong G. Y. C., A modified semi-parametric MLE in linear regression analysis with complete data and right-censored data, Technometrics (under revision)
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Supported by the U.S. Army Grants DAMD17-99-1-9390 and DAMD17-01-0448.
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Yu, Q.Q., Wong, G.Y.C. Asymptotic Properties of a Modified Semi-Parametric MLE in Linear Regression with Right-Censored Data. Acta Math Sinica 18, 405–416 (2002). https://doi.org/10.1007/s101140200169
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DOI: https://doi.org/10.1007/s101140200169