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Abstract We propose an efficient estimator for the coefficients in censored quantile regression using the envelope model. The envelope model uses dimension reduction techniques to identify material and immaterial components in the data, and forms the estimator based only on the material component, thus reducing the variability of estimation. We will demonstrate the guaranteed asymptotic efficiency gain of our proposed envelope estimator over the traditional estimator for censored quantile regression. Our analysis begins with the local weighing approach that traditionally relies on semiparametric ‐estimation involving the conditional Kaplan–Meier estimator. We will instead invoke the independent identically distributed (i.i.d.) representation of the Kaplan–Meier estimator, which eliminates this infinite‐dimensional nuisance and transforms our objective function in ‐estimation into a ‐process indexed by only an Euclidean parameter. The modified ‐estimation problem becomes entirely parametric and hence more amenable to analysis. We will also reconsider the i.i.d. representation of the conditional Kaplan–Meier estimator.
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Confidence bands for survival curves from outcome‐dependent stratified samples
Abstract We consider the construction of confidence bands for survival curves under the outcome‐dependent stratified sampling. A main challenge of this design is that data are a biased dependent sample due to stratification and sampling without replacement. Most literature on regression approximates this design by Bernoulli sampling but variance is generally overestimated. Even with this approximation, the limiting distribution of the inverse probability weighted Kaplan–Meier estimator involves a general Gaussian process, and hence quantiles of its supremum is not analytically available. In this paper, we provide a rigorous asymptotic theory for the weighted Kaplan–Meier estimator accounting for dependence in the sample. We propose the novel hybrid method to both simulate and bootstrap parts of the limiting process to compute confidence bands with asymptotically correct coverage probability. Simulation study indicates that the proposed bands are appropriate for practical use. A Wilms tumor example is presented.
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- Award ID(s):
- 2014971
- PAR ID:
- 10539928
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Scandinavian Journal of Statistics
- Volume:
- 51
- Issue:
- 3
- ISSN:
- 0303-6898
- Page Range / eLocation ID:
- 1086 to 1102
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1111/sjos.12700
