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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)

- Jon A. Wellner, Ying Zhang
- 1998

We study two estimators of the mean function of a counting process based on panel count data The setting for panel count data is one in which n independent subjects each with a counting process with common mean function are observed at several possibly di erent times during a study Following a model proposed by Schick and Yu we allow the number of… (More)

- Jon A. Wellner, Ying Zhang
- 2005

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)

- Jian Huang, Jon A. Wellner
- 1995

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)

- Jian Huang, Jon A. Wellner
- 1996

We review estimation in interval censoring models including nonparametric esti mation of a distribution function and estimation of regression models In the non parametric setting we describe computational procedures and asymptotic properties of the nonparametric maximum likelihood estimators In the regression setting we focus on the proportional hazards the… (More)

By Leah Jager∗ and Jon A. Wellner† Grinnell College and University of Washington A unified family of goodness-of-fit tests based on φ−divergences is introduced and studied. The new family of test statistics Sn(s) includes both the supremum version of the Anderson-Darling statistic and the test statistic of Berk and Jones (1979) as special cases (s = 2 and s… (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)