In this paper we propose a test statistic to discriminate between models with finite variance and models with infinite variance. The test statistic is the ratio of the sample standard deviation and the sample interquartile range. Both asymptotic and finite sample properties of the test statistic...

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,...

Theorems of approximation of Gaussian processes for the sequential empirical process of the permutations of independent random variables are established. The results are applied to simulate critical values for the functionals of sequential empirical processes used in change point analysis. The...

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...

Let X1,...,Xn be jointly Gaussian random variables with mean zero. It is shown that [for all]x>0 and [for all]1[less-than-or-equals, slant]k<nandwhere [rho]=([Sigma]/([Sigma]11 [Sigma]22))1/2, [Sigma],[Sigma]11 and [Sigma]22 are the covariance matrices of (X1,...,Xn), (X1,...,Xk) and (Xk+1,...,Xn), respectively. In particular, for fractional Brownian motion {X(t),t[greater-or-equal, slanted]0} of order [alpha] (0<[alpha]<1), there exists d[alpha]>0 such that for any 0<a<b, x>0 and y>0. As an application, it is proved that the small ball constant for the fractional Brownian motion of order [alpha] exists.