The Bernstein–von Mises theorem in semiparametric competing risks models

Semiparametric analysis of mixture regression models with competing risks data.

In the analysis of competing risks data, cumulative incidence function is a useful summary of the overall crude risk for a failure type of interest. Mixture regression modeling has served as a natural approach to performing covariate analysis based on this quantity. However, existing mixture regression methods with competing risks data either impose parametric assumptions on the conditional ris...

SEMIPARAMETRIC ESTIMATORS IN COMPETING RISKS REGRESSION by

A semiparametric Bernstein - von Mises theorem for Gaussian process priors

This paper is a contribution to the Bayesian theory of semiparametric estimation. We are interested in the so-called Bernstein-von Mises theorem, in a semiparametric framework where the unknown quantity is (θ , f ), with θ the parameter of interest and f an infinite-dimensional nuisance parameter. Two theorems are established, one in the case with no loss of information and one in the informati...

Efficient Estimation of Semiparametric Transformation Models for the Cumulative Incidence of Competing Risks.

The cumulative incidence is the probability of failure from the cause of interest over a certain time period in the presence of other risks. A semiparametric regression model proposed by Fine and Gray (1999) has become the method of choice for formulating the effects of covariates on the cumulative incidence. Its estimation, however, requires modeling of the censoring distribution and is not st...

Quadratic semiparametric Von Mises calculus.

We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching c...