In this paper, some nonparametric approaches of density function estimation are developed when censoring indicators are missing at random. A conditional mean score based estimator and a mean score estimator are suggested, respectively. The two estimators are proved to be asymptotically normal...

Let F and G be multivariate probability distribution functions, each with equal one dimensional marginals, such that there exists a sequence of constants an 0, n [set membership, variant] , with [formula] for all continuity points (x1, ..., xd) of G. The distribution function G is characterized...

An asymptotic theory is developed for the estimation of high quantile curves, i.e., sets of points in higher dimensional space for which the exeedance probability is pn, with npn -- 0 (n -- [infinity]). Here n is the number of available observations. This is the situation of interest if one...

A simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, Liu and Hayter [W. Liu, A.J. Hayter, Minimum area confidence set...

In this paper a theorem on gambling systems for Bernoulli sequences is extended to arbitrary binary random sequences by using the notion of the likelihood ratio, and an analytical technique for the study of a.e. convergence is presented.