In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model [D.R. Cox, Regression models and life tables (with discussion), Journal of the Royal Statistical Society, Series B 34 (1972) 187-220; D.R. Cox, Partial likelihood,...

In this paper, we carry out an in-depth theoretical investigation of Bayesian inference for the Cox regression model. We establish necessary and sufficient conditions for posterior propriety of the regression coefficient, β, in Cox's partial likelihood, which can be obtained as the limiting...

In this article, we model multivariate categorical (binary and ordinal) response data using a very rich class of scale mixture of multivariate normal (SMMVN) link functions to accommodate heavy tailed distributions. We consider both noninformative as well as informative prior distributions for...

This paper proves that the law of the iterated logarithm holds for a stationary negatively associated sequence of random variables with finite variance. The proof is based on a Rosenthal type maximal inequality, a Kolmogorov type exponential inequality and Stein's method.

We prove that the directed random walk satisfies the strong law of large numbers if and only if the environment has a finite mean.

We find a necessary and sufficient condition for the weak convergence of the uniform empirical and quantile processes to a Brownian bridge in weighted Lp-distances. Under the same condition, weighted Lp-functionals of the uniform empirical and quantile processes converge in distribution to the...

We propose a circular block resampling procedure to modify Künsch's moving block bootstrap. Our procedure has the special feature that the resampled data are like drawing from the empirical distribution function of dependent observations. No information is lost concerning the nature of...

We establish upper bounds for moduli of continuity of the local times of Gaussian processes with stationary increments and for those of stationary Gaussian processes.