Let (Ut,Vt) be a bivariate Lévy process, where Vt is a subordinator and Ut is a Lévy process formed by randomly weighting each jump of Vt by an independent random variable Xt having cdf F. We investigate the asymptotic distribution of the self-normalized Lévy process Ut/Vt at 0 and at ∞. We...

We propose Bayesian model selection based on composite datasets, which can be constructed from various subsample estimates. The method remains consistent without fully specifying a probability model, and is useful for dependent data, when asymptotic variance of the parameter estimator is...

Let be a linear process, where and [var epsilon]t, t[set membership, variant]Z, are i.i.d. r.v.'s in the domain of attraction of a normal law with zero mean and possibly infinite variance. We prove a central limit theorem for self-normalized sums where is a sum of squares of block-sums of size...

In statistical analyses the complexity of a chosen model is often related to the size of available data. One important question is whether the asymptotic distribution of the parameter estimates normally derived by taking the sample size to infinity for a fixed number of parameters would remain...