Input modeling software tries to fit standard probability distributions to data assuming that the data are independent. However, the input environment can generate correlated data. Ignoring the correlations might lead to serious inaccuracies in the performance measures. In the past few years, several dependence modeling packages with different properties have been developed. In our dissertation...

Autoregressive models are reviewed for the analysis of multivariate count time series. A particular topic interest which is discussed in detail that choice a suitable distribution vectors random variables. The focus on three main approaches taken series analysis: (a) integer autoregressive processes, (b) parameter-driven and (c) observation-driven models. aim to highlight some recent methodolog...

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X = A+BWC for positive integer s and real t, whereW is a standard normal random vector and A, B, C are appropriately dimensioned constantmatrices.We solve the problems by amatrix product scalarization technique and interpret the solutions in system-theoretic terms. The results...

2 Preliminaries 7 2.1 Matrices and their singular values . . . . . . . . . . . . . . . . . . 7 2.2 Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Sub-gaussian random variables . . . . . . . . . . . . . . . . . . . 9 2.4 Sub-exponential random variables . . . . . . . . . . . . . . . . . . 14 2.5 Isotropic random vectors . . . . . . . . . . . . . . . . . . . . . . ...

The structure of non-Gaussian autoregressive schemes is described. Asymptotically efficient methods for the estimation of the coefficients of the models are described under appropriate conditions, some of which relate to smoothness and positivity of the density function f of the independent random variables generating the process. The principal interest is in nonminimum phase models.

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian αstable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are n-consistent ...

We present a new version (> 2.0) of the hglm package for fitting hierarchical generalized linear models (HGLMs) with spatially correlated random effects. CAR() and SAR() families for conditional and simultaneous autoregressive random effects were implemented. Eigen decomposition of the matrix describing the spatial structure (e.g., the neighborhood matrix) was used to transform the CAR/SAR rand...