Integer valued AR (INAR) processes are perfectly suited for modelling count data. We consider the inclusion of explanatory variables into the INAR model to extend the applicability of INAR models and give an alternative to Poisson regression models. An efficient MCMC algorithm is constructed to analyze the model and incorporates both explanatory variable and order selection. The methodology is ...

Given an integer function f , the problem is to find its best uniform approximation from a set K of integervalued bounded functions. Under certain conditions on K , the best extremal (maximal or minimal) approximation is identified. Furthermore, the operator mapping f to its extremal best approximation is shown to be Lipschitzian with some constant C or optimal Lipschitzian having the smallest ...

The purpose of this paper is to introduce and develop a family of Z+-valued autoregressive processes of order p (INAR(p)) by using the generalized multiplication F of van Harn and Steutel (1982). We obtain various distributional and regression properties for these models. A number of stationary INAR(p) processes with specific marginals are presented and are shown to generalize several existing ...

Every integer is either even or odd, so we know that the polynomial f(x) = x(x− 1) 2 is integervalued on the integers, even though its coefficients are not in Z. Similarly, since every binomial coefficient ( k n ) is an integer, the polynomial ( x n ) = x(x− 1)...(x− n+ 1) n! must also be integervalued. These polynomials were used for polynomial interpolation as far back as the 17 century. Inte...

We show that every henselian valued field L of residue characteristic 0 admits a proper subfield K which is dense in L. We present conditions under which this can be taken such that L|K is transcendental and K is henselian. These results are of interest for the investigation of integer parts of ordered fields. We present examples of real closed fields which are larger than the quotient fields o...

The paper is devoted to the problem of integer-valued estimating of information quantity in a pixel of digital image. The definition of an integer estimation of information quantity based on constructing of the certain binary hierarchy of pixel clusters is proposed. The methods for constructing hierarchies of clusters and generating of hierarchical sequences of image approximations that minimal...

Results are given for aggregating a system of nonnegative integer equations of the form Xj = bj, je N, to yield a single equivalent equation whose coefficients correspond to those of the best previously known result for the special case b, = 1, jc,V. Different aggregations are obtained for different permutations of the indexes jEIV, according to the sizes of the b, values, and we also identify ...