Median regression using nonparametric kernel estimation

The fitting of heteroscedastic median regression models to right censored data has been a topic of much research in survival analysis in recent years. McKeague et al. (2001) used the missing information principle to propose an estimator for the regression parameters, and derived the asymptotic properties of their estimator assuming that the covariate takes values in a finite set. In this paper the large sample properties of their estimator are derived when the covariate is continuous. A kernel conditional Kaplan-Meier estimator is used in the missing information principle estimating function. A simulation study involving a one-dimensional covariate is presented.

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

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

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

[4]  N. Breslow,et al.  A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship , 1974 .

[5]  Anna Lindgren,et al.  Quantile regression with censored data using generalized L 1 minimization , 1997 .

[6]  E. Giné,et al.  Rates of strong uniform consistency for multivariate kernel density estimators , 2002 .

[7]  Sundarraman Subramanian,et al.  Median regression and the missing information principle , 2001 .

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

[9]  K. Knight Comparing Conditional Quantile Estimators: Rst and Second Order Considerations , 2022 .

[10]  Stephen Portnoy,et al.  Censored Regression Quantiles , 2003 .

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

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

[13]  W. Stute A Law of the Logarithm for Kernel Density Estimators , 1982 .

[14]  Ing Rj Ser Approximation Theorems of Mathematical Statistics , 1980 .

[15]  R. Koenker,et al.  Asymptotic Theory of Least Absolute Error Regression , 1978 .

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