Regression M-estimators with doubly censored data

Partial rank estimation of duration models with general forms of censoring

“…For a regression model with double censoring, estimators have been proposed by Zhang andLi, 1996, Ren andGu, 1997 to name a few. Both of these require a linear regression specification and the censoring variables to be independent of the covariates.…”

Estimation and goodness-of-fit for the Cox model with various types of censored data

“…H n (z) of sample Z 1 ,y,Z n , obtainĜ n ðx,zÞ through computingĜ n ðx,Z k Þ ¼F XjZ k ðxÞH n ðZ k Þ for all 1 rk rn. Under regularity conditions, Ren and Gu (1997) showed that ffiffiffi n p ðĜ n ÀGÞ is asymptotically centered Gaussian, i.e., assumption (AS2) of Theorem 2 holds forĜ n by Ren and Gu (1997). Thus, Theorem 2 holds for doubly censored data (3.6).…”

“…For doubly censored data (3.6), Ren and Gu (1997) constructed a nonparametric estimatorĜ n ðx,zÞ for bivariate d.f. G(x,z) as follows.…”

“…For the case that the response variable X in (1.2) is subject to interval censoring Case 1 or Case 2 as described in Groeneboom and Wellner (1992), there have been the works on the estimation of b 0 by Finkelstein (1986), Satten (1996), Huang (1997), among others. However, the approaches developed for right censored data and interval censored data do not have direct extension to other complicated types of censored data, such as doubly censored data (Turnbull, 1974;Chang and Yang, 1987;Gu and Zhang, 1993;Ren and Gu, 1997), partly interval-censored data (Huang, 1999), bivariate right censored data (Dabrowska, 1989), bivariate data under univariate right censoring (Lin and Ying, 1993), etc., for which there have not been any published works on the estimation of b 0 . Also, for these complicated types of censored data as well as for above mentioned interval censored Case 1 or Case 2 data, there have been no works on the testing methods to assess the goodness-of-fit for the Cox model (1.1).…”

Asymptotic properties for an M-estimator of the regression function with truncation and dependent data

“…Under censored model, there is some literature on the M-estimators. For example, Ren and Gu (1997) proposed the M-estimators for the linear regression model with random design when the response observations are doubly censored. Jin (2007) constructed the M-estimators of regression parameters in semiparametric linear models for censored data and established asymptotic normality of the estimators.…”