2,877 research outputs found
Comparing Survival Curves Using Rank Tests
Survival times of patients can be compared using rank tests in various experimental setups, including the two-sample case and the case of paired data. Attention is focussed on two frequently occurring complications in medical applications: censoring and tail alternatives. A review is given of the author's recent work on a new and simple class of censored rank tests. Various models for tail alternatives are discussed and the relation to censoring is demonstrated
Large-sample study of the kernel density estimators under multiplicative censoring
The multiplicative censoring model introduced in Vardi [Biometrika 76 (1989)
751--761] is an incomplete data problem whereby two independent samples from
the lifetime distribution , and
, are observed subject to a form of coarsening.
Specifically, sample is fully observed while
is observed instead of , where
and is an independent sample from the standard
uniform distribution. Vardi [Biometrika 76 (1989) 751--761] showed that this
model unifies several important statistical problems, such as the deconvolution
of an exponential random variable, estimation under a decreasing density
constraint and an estimation problem in renewal processes. In this paper, we
establish the large-sample properties of kernel density estimators under the
multiplicative censoring model. We first construct a strong approximation for
the process , where is a solution of the
nonparametric score equation based on , and
is the total sample size. Using this strong approximation and a result
on the global modulus of continuity, we establish conditions for the strong
uniform consistency of kernel density estimators. We also make use of this
strong approximation to study the weak convergence and integrated squared error
properties of these estimators. We conclude by extending our results to the
setting of length-biased sampling.Comment: Published in at http://dx.doi.org/10.1214/11-AOS954 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Smooth plug-in inverse estimators in the current status continuous mark model
We consider the problem of estimating the joint distribution function of the
event time and a continuous mark variable when the event time is subject to
interval censoring case 1 and the continuous mark variable is only observed in
case the event occurred before the time of inspection. The nonparametric
maximum likelihood estimator in this model is known to be inconsistent. We
study two alternative smooth estimators, based on the explicit (inverse)
expression of the distribution function of interest in terms of the density of
the observable vector. We derive the pointwise asymptotic distribution of both
estimators.Comment: 29 pages, 12 figure
Optimally combining Censored and Uncensored Datasets
We develop a simple semiparametric framework for combining censored and uncensored samples so that the resulting estimators are consistent, asymptotically normal, and use all information optimally. No nonparametric smoothing is required to implement our estimators. To illustrate our results in an empirical setting, we show how to estimate the effect of changes in compulsory schooling laws on age at first marriage, a variable that is censored for younger individuals. Results from a small simulation experiment suggest that the estimator proposed in this paper can work very well in finite samples.
Semiparametric Estimation of Single-Index Transition Intensities
This research develops semiparametric kernel-based estimators of state-specific conditional transition intensitiesm, hs (y|x), for duration models with right-censoring and/or multiple destinations (competing risks). Both discrete and continous duration data are considered. The maintained assumptions are that hs(y|x) depends on x only through an index x'Bs. In contrast to existing semiparametric estimators, proportional intensities is not assumed. The new estimators are asymptotically normally distributed. The estimator of Bs is root-n consistent. The estimator of hs (y|x) achieves the one-dimensional rate of convergence. Thus the single-index assumption eliminates the "curse of dimensionality". The estimators perform well in Monte Carlo experiments.semiparametric estimation; kernel regression; duration analysis; competing risks; censoring
- …