147 research outputs found
Discussion of: Brownian distance covariance
We discuss briefly the very interesting concept of Brownian distance
covariance developed by Sz\'{e}kely and Rizzo [Ann. Appl. Statist. (2009), to
appear] and describe two possible extensions. The first extension is for high
dimensional data that can be coerced into a Hilbert space, including certain
high throughput screening and functional data settings. The second extension
involves very simple modifications that may yield increased power in some
settings. We commend Sz\'{e}kely and Rizzo for their very interesting work and
recognize that this general idea has potential to have a large impact on the
way in which statisticians evaluate dependency in data. [arXiv:1010.0297]Comment: Published in at http://dx.doi.org/10.1214/09-AOAS312B the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org). With Correction
Q-learning with censored data
We develop methodology for a multistage decision problem with flexible number
of stages in which the rewards are survival times that are subject to
censoring. We present a novel Q-learning algorithm that is adjusted for
censored data and allows a flexible number of stages. We provide finite sample
bounds on the generalization error of the policy learned by the algorithm, and
show that when the optimal Q-function belongs to the approximation space, the
expected survival time for policies obtained by the algorithm converges to that
of the optimal policy. We simulate a multistage clinical trial with flexible
number of stages and apply the proposed censored-Q-learning algorithm to find
individualized treatment regimens. The methodology presented in this paper has
implications in the design of personalized medicine trials in cancer and in
other life-threatening diseases.Comment: Published in at http://dx.doi.org/10.1214/12-AOS968 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Higher order semiparametric frequentist inference with the profile sampler
We consider higher order frequentist inference for the parametric component
of a semiparametric model based on sampling from the posterior profile
distribution. The first order validity of this procedure established by Lee,
Kosorok and Fine in [J. American Statist. Assoc. 100 (2005) 960--969] is
extended to second-order validity in the setting where the infinite-dimensional
nuisance parameter achieves the parametric rate. Specifically, we obtain higher
order estimates of the maximum profile likelihood estimator and of the
efficient Fisher information. Moreover, we prove that an exact frequentist
confidence interval for the parametric component at level can be
estimated by the -level credible set from the profile sampler with an
error of order . Simulation studies are used to assess
second-order asymptotic validity of the profile sampler. As far as we are
aware, these are the first higher order accuracy results for semiparametric
frequentist inference.Comment: Published in at http://dx.doi.org/10.1214/07-AOS523 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Penalized log-likelihood estimation for partly linear transformation models with current status data
We consider partly linear transformation models applied to current status
data. The unknown quantities are the transformation function, a linear
regression parameter and a nonparametric regression effect. It is shown that
the penalized MLE for the regression parameter is asymptotically normal and
efficient and converges at the parametric rate, although the penalized MLE for
the transformation function and nonparametric regression effect are only
consistent. Inference for the regression parameter based on a block
jackknife is investigated. We also study computational issues and demonstrate
the proposed methodology with a simulation study. The transformation models and
partly linear regression terms, coupled with new estimation and inference
techniques, provide flexible alternatives to the Cox model for current status
data analysis.Comment: Published at http://dx.doi.org/10.1214/009053605000000444 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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