ﻻ يوجد ملخص باللغة العربية
Integer-valued time series models have been a recurrent theme considered in many papers in the last three decades, but only a few of them have dealt with models on $mathbb Z$ (that is, including both negative and positive integers). Our aim in this paper is to introduce a first-order integer-valued autoregressive process on $mathbb Z$ with skew discrete Laplace marginals (Kozubowski and Inusah, 2006). For this, we define a new operator that acts on two independent latent processes, similarly as made by Freeland (2010). We derive some joint and conditional basic properties of the proposed process such as characteristic function, moments, higher-order moments and jumps. Estimators for the parameters of our model are proposed and their asymptotic normality are established. We run a Monte Carlo simulation to evaluate the finite-sample performance of these estimators. In order to illustrate the potentiality of our process, we apply it to a real data set about population increase rates.
An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound Poisson distribution.
We propose a novel generalisation to the Student-t Probabilistic Principal Component methodology which: (1) accounts for an asymmetric distribution of the observation data; (2) is a framework for grouped and generalised multiple-degree-of-freedom str
We propose a latent topic model with a Markovian transition for process data, which consist of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem solv
Many social and other networks exhibit stable size scaling relationships, such that features such as mean degree or reciprocation rates change slowly or are approximately constant as the number of vertices increases. Statistical network models built
We demonstrate a method for localizing where two smooths differ using a true discovery proportion (TDP) based interpretation. The procedure yields a statement on the proportion of some region where true differences exist between two smooths, which re