Abstract
The least absolute deviations (LAD) estimation for nonlinear regression models with randomly censored data is studied and the asymptotic properties of LAD estimators such as consistency, boundedness in probability and asymptotic normality are established. Simulation results show that for the problems with censored data, LAD estimation performs much more robustly than the least squares estimation.
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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.
Koul, H., Susarla, V., Van Ryzin, J., Regression analysis with randomly right-censored data, Ann. Stat., 1981, 9: 1276–1288.
Chatterjee, S., McLeish, D. L., Fitting linear regression models to censored data by least squares and maximum likelihood methods, Comm. Statist-Theor. Meth., 1986, 15: 3227–3243.
Leurgans, S., Linear models, random censoring and synthetic data, Biometrika, 1987, 74: 301–309.
Heller, G., Simonoff, J., A comparison of estimators for regression with censored response variable, Biometrika, 1990, 77(3): 515–520.
Kaplan, E. L., Meier, P., Nonparametric estimation from incomplete observations, J. Am. Statist. Assoc., 1958, 53: 457–481.
James, I. R., Smith, P. J., Consistency results for linear regression with censored data, Ann. Stat., 1984, 12: 590–600.
Smith, P. J., Asymptotic properties of linear regression estimators under a fixed censorship model, Aust. J. Statist., 1988, 30: 52–66.
Powell, J. L., Least absolute deviations estimation for the censored regression model, J. Econometrics, 1984, 25: 303–325.
Powell, J. L., Censored regression quantiles, J. Econometrics, 1986, 32: 143–155.
Rao, C. R., Zhao, L. C., Asymptotic normility of LAD estimator in censored regression models, Math. Methods of Statist., 1993, 2(3): 228–239.
Chen, X. R., Wu, Y. H., Consistency of L1 estimates in censored linear regression models, Commu. Statist-Theor. Meth., 1993, 23(7): 1847–1858.
Yang, G. L., Some recent development in nonparametric inference for right censored and randomly truncated data, in Statistics for the 21st Century (eds. Rao, C. R., Székeley, G. J.), New York: Marcel Dekker, 2000, 441–457.
Whittle, P., Bounds for the moments of linear and quadratic forms in independent variables, Theory of Probab. and Appl., 1960, 5: 302–305.
Prakasa Rao, B. L. S., On the rate of convergence of least squares estimator in nonlinear regression model for multiparameter, J. Ramanujan Math. Soc., 1987, 1: 109–123.
Zhou, X. Q., Wang, J. D., A genetic method of LAD estimation for models with censored data, Computational Statistics and Data Analysis, 2005, 48(3): 451–466.
Davis, R., Knight, K., Liu, J., M-estimation for autoregressions with infinite variance, Stochastic Processes Appl., 1992, 40: 145–180.
Prakasa Rao, B. L. S., ed., Asymptotic Theory of Statistical Inference, New York: Wiley, 1987.
Wang, J. D., Asymptotic normality of L1-estimators in nonlinear regression, J. Multivariate Analysis, 1995, 54: 227–238.
Wang, J. D., Asymptotics of least square estimators in constrained nonlinear regression, Ann. Stat., 1996, 24: 1316–1326.
Wu, J. F., Asymptotic theory of nonlinear least squares estimation, Ann. Stat., 1981, 9: 501–513.
Prakasa Rao, B. L. S., Tightness of probability measures generated by stochastic processes on metric spaces, Bull. Inst. Math. Acad. Sinica, 1975, 3: 353–367.
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Xiuqing, Z., Jinde, W. LAD estimation for nonlinear regression models with randomly censored data. Sci. China Ser. A-Math. 48, 880–897 (2005). https://doi.org/10.1007/BF02879071
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DOI: https://doi.org/10.1007/BF02879071