Median regression and the missing information principle

Median regression analysis has robustness properties which make it an attractive alternative to regression based on the mean.In this paper,the missing information principle is applied to a right-censored version of the median regression model,leading to a new estimator for the regression parameters.Our approach adapts Efton's derivation of self-consistency for the Kaplan-Meier estimator to the context of median regression;we replace the least absolute deviation estimating function by its (estimated) conditional expectation given the data.For discrete covariates the new estimator is shown to be asymptotically equivalent to anad hocestimator introduced by Ying,Jung and Wei,and to have improved moderate-sample performance in simulation studies.

[1]  M. Woodbury.  A missing information principle: theory and applications , 1972 .

[2]  Zhiliang Ying,et al.  A Missing Information Principle and $M$-Estimators in Regression Analysis with Censored and Truncated Data , 1994 .

[3]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[4]  Song Yang,et al.  Censored Median Regression Using Weighted Empirical Survival and Hazard Functions , 1999 .

[5]  J. Wellner,et al.  Information Bounds and Nonparametric Maximum Likelihood Estimation , 1992 .

[6]  R. Gill.  Non- and semi-parametric maximum likelihood estimators and the Von Mises method , 1986 .

[7]  J. Crowley,et al.  A Large Sample Study of Generalized Maximum Likelihood Estimators from Incomplete Data Via Self-Consistency , 1985 .

[8]  Paul Meier,et al.  Estimation of a Distribution Function from Incomplete Observations , 1975, Journal of Applied Probability.

[9]  Hani Doss,et al.  Confidence Bands for the Median Survival Time as a Function of the Covariates in the Cox Model , 1993 .

[10]  B. Efron.  The two sample problem with censored data , 1967 .

[11]  R. Gill.  Censoring and stochastic integrals , 1980 .

[12]  J. Robins,et al.  Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. , 1997, Statistics in medicine.

[13]  Zhiliang Ying,et al.  Survival analysis with median regression models , 1995 .

[14]  Hani Doss,et al.  An Elementary Approach to Weak Convergence for Quantile Processes, with Applications to Censored Survival Data , 1992 .

[15]  Sin-Ho Jung.  Quasi-Likelihood for Median Regression Models , 1996 .

[16]  James M. Robins.  Locally Efficient Median Regression with Random Censoring and Surrogate Markers , 1996 .

[17]  Dorota M. Dabrowska,et al.  Uniform Consistency of the Kernel Conditional Kaplan-Meier Estimate , 1989 .

[18]  James L. Powell,et al.  Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions , 1990, Econometric Theory.