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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

- 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 diierent times during a study. F ollowing a model proposed by S c hick and Yu (1997), we allow the… (More)

We study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function. The likelihood ratio test for this hypothesis is derived in the particular case of interval censoring (or current status data) and its limiting distribution is obtained. The limiting distribution is that of the integral of the… (More)

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)

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.… (More)

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- 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 proole likelihood methods using Groeneboom's iterative convex minorant algorithm. Under appropriate regularity conditions, the maximum likelihood estimator for the regression parameter is shown to be asymptotically… (More)

- Jon A. Wellner
- 1995

The likelihood ratio statistic for testing pointwise hypotheses about the survival time distribution in the current status model can be inverted to yield confidence intervals (CIs). One advantage of this procedure is that CIs can be formed without estimating the unknown parameters that figure in the asymptotic distribution of the maximum likelihood… (More)

- Anne Sheehy, Jon A. Wellner, UNIFORM DONSKER
- 1990

A class F of measurable functions' on a probability space (A ,fl ,p) is called a P-Donsker class, and we also write F E CLT (P), if the empirical processes X: == {;; (JPn-P) converge weakly to a P-Brownian bridge Gp. If this convergence holds for every probability measure P on (A,i4.), then F is called a universal Donsker class, and we write F E CLT(M)… (More)