Empirical processes for non ergodic data are investigated under uniform distance. Some CLT’s, both uniform and non uniform, are proved. In particular, conditions for the empirical process Bn = √ n(μn − bn) to converge in distribution are given, where μn is the empirical measure and bn the arithmetic mean of the first n predictive measures. Such conditions apply under various assumptions on the ...

Sufficient conditions are given under which the absolute continuity of joint distribution conditionally independent random variables can be violated. It is shown that in case a dimension n>1 this occurs for sufficiently large number discontinuity points one-dimensional conditional distributions.

We introduce a new model for building conditional generative models in a semisupervised setting to conditionally generate data given attributes by adapting the GAN framework. The proposed semi-supervised GAN (SS-GAN) model uses a pair of stacked discriminators to learn the marginal distribution of the data, and the conditional distribution of the attributes given the data respectively. In the s...

This study considers the goodness of fit test for a class of conditionally heteroscedastic location-scale time series models. For this task, we develop an entropy-type goodness of fit test based on residuals. To examine the asymptotic behavior of the test, we first investigate the asymptotic property of the residual empirical process and then derive the limiting null distribution of the entropy...

The probability density function of a multiparameter multinomial distribution can be expressed in terms of the permanent of a suitable matrix. This fact and certain results on conditionally negative definite matrices are used to prove a conjecture due to Karlin and Rinott.

We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for developing a conditionally Gaussian approximation to the loss distribution. Numerical results illustrate the accuracy and computational efficiency of the app...

When a Bayesian version of the general linear mixed model is created by adopting a conditionally conjugate prior distribution, a simple block Gibbs sampler can be employed to explore the resulting intractable posterior density. In this article it is shown that, under mild conditions that nearly always hold in practice, the block Gibbs Markov chain is geometrically ergodic.

Form an $n \times n$ matrix by drawing entries independently from $\{\pm1\}$ (or another fixed nontrivial finitely supported distribution in $\mathbf{Z}$) and let $\phi$ be the characteristic polynomial. Conditionally on extended Riemann hypothesis, with high probability is irreducible $\mathrm{Gal}(\phi) \geq A_n$.