Jon A. Wellner

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We study nonparametric estimation of convex regression and density functions by methods of least squares (in the regression and density cases) and maximum likelihood (in the density estimation case). We provide characterizations of these estimators, prove that they are consistent and establish their asymptotic distributions at a fixed point of positive(More)
We consider estimation in a particular semiparametric regression model for the mean of a counting process with “panel count” data. The basic model assumption is that the conditional mean function of the counting process is of the form E{N(t)|Z} = exp(β 0 Z)Λ0(t) where Z is a vector of covariates and Λ0 is the baseline mean function. The “panel count”(More)
A distribution which arises in problems of estimation of monotone functions is that of the location of the maximum of two-sided Brownian motion minus a parabola. Using results of Groeneboom (1985), (1989), we present algorithms and programs for computation of this distribution and its quantiles. We also present some comparisons with earlier computations(More)
A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian motion. Its(More)
Weighted likelihood, in which one solves Horvitz-Thompson or inverse probability weighted (IPW) versions of the likelihood equations, offers a simple and robust method for fitting models to two phase stratified samples. We consider semiparametric models for which solution of infinite dimensional estimating equations leads to √ N consistent and(More)
Maximum likelihood estimation for the proportional hazards model with interval censored data is considered The estimators are computed by pro le likelihood methods using Groeneboom s iterative convexminorant algorithm Under appropriate regularity conditions the maximum likelihood estimator for the regression parameter is shown to be asymptotically normal(More)
type, all depending on an additional parameter which assumes a particular value for the problem in question. The relationship between this idea and dynamic programming, which is a technique for dealing with problems in which many decisions must be made, often sequentially, to maximise or minimise a quantity of interest, is deferred until the end of the(More)