There has been much interest recently in the specially constructed empirical processes of Komlós, Major and Tusnády [2]; as one would guess, much of the application has come from the Hungarian school. In this note we contribute to the unifying effect this profound work has had by showing how...

NSF, NIAID

Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the...

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under Lp norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p<d/(d-1) and p>d/(d-1). We apply the new bounds...</d/(d-1)>

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...

We consider semiparametric models for which solution of Horvitz-Thompson or inverse probability weighted (IPW) likelihood equations with two-phase stratified samples leads to <formula format="inline"><file name="sjos_523_mu1.gif" type="gif" /></formula> consistent and asymptotically Gaussian estimators of both Euclidean and non-parametric parameters. For Bernoulli...

We state and prove a limit theorem for estimators of a general, possibly infinite dimensional parameter based on unbiased estimating equations containing estimated nuisance parameters. The theorem corrects a gap in the proof of one of the assertions of our paper 'Weighted likelihood for...