An explicit formula for the correlation coefficient in a two-dimensional AR(1) process is derived. Approximate critical values for the correlation coefficient between two one-dimensional AR(1) processes are tabulated. They are based on Bartlett’s approximation and on an asymptotic distribution derived by McGregor. The results are compared with critical values obtained from a simulation study.
The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol–Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied...
Given two initial points generating monotone convergent Brown iterations in the context of the monotone Newton theorem (MNT), it is proved that if one of them is an upper bound of the other, then the same holds for each pair of respective terms in the Brown sequences they generate. This comparison result is carried over to the corresponding Brown-Fourier iterations. An illustration is discussed.
An iterative procedure for computation of stationary density of autoregressive processes is proposed. On an example with exponentially distributed white noise it is demonstrated that the procedure converges geometrically fast. The AR(1) and AR(2) models are analyzed in detail.
We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these...
The knowledge of causal relations provides a possibility to perform predictions and helps to decide about the most reasonable actions aiming at the desired objectives. Although the causal reasoning appears to be natural for the human thinking, most of the traditional statistical methods fail to address this issue. One of the well-known methodologies correctly representing the relations of cause and effect is Pearl's causality approach. The paper brings an alternative, purely algebraic methodology...