An efficient estimator for the expectation $\int fP̣$ is constructed, where $P$ is a Gibbs random field, and $f$ is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.

Let A = (aij) be an n x n matrix defined by aij = aji = i, i = 1,...,n. This paper gives some elementary properties of A and other related matrices. The eigenstructure of A is conjectured: given an eigenvector v of A the remaining eigenvectors are obtained by permuting up to sign the components of v. This problem arises in a distance based method applied to non linear regression.

Variable annuities contain complex guarantees, whose fair market value cannot be calculated in closed form. To value the guarantees, insurance companies rely heavily on Monte Carlo simulation, which is extremely computationally demanding for large portfolios of variable annuity policies. Metamodeling approaches have been proposed to address these computational issues. An important step of metamodeling approaches is the experimental design that selects a small number of representative variable annuity...

This paper compares five small area estimators. We use Monte Carlo simulation in the context of both artificial and real populations. In addition to the direct and indirect estimators, we consider the optimal composite estimator with population weights, and two composite estimators with estimated weights: one that assumes homogeneity of within area variance and squared bias and one that uses area-specific estimates of variance and squared bias. In the study with real population, we found that among...

Let ${𝕖}_t={(e_{t1},\cdots ,e_{tp})}^{\text{'}}$ be a $p$-dimensional nonnegative strict white noise with finite second moments. Let $h_{ij}\left(x\right)$ be nondecreasing functions from $[0,\infty )$ onto $[0,\infty )$ such that $h_{ij}\left(x\right)\le x$ for $i,j=1,\cdots ,p$. Let $𝕌=\left(u_{ij}\right)$ be a $p\times p$ matrix with nonnegative elements having all its roots inside the unit circle. Define a process ${𝕏}_t={(X_{t1},\cdots ,X_{tp})}^{\text{'}}$ by $$X_{tj}=u_{j1}{h}_{1j}\left(X_{t-1,1}\right)+\cdots +u_{jp}{h}_{pj}\left(X_{t-1,p}\right)+e_{tj}$$ for $j=1,\cdots ,p$. A method for estimating $𝕌$ from a realization ${𝕏}_1,\cdots ,{𝕏}_n$ is proposed. It is proved that the estimators are strongly consistent.

If n independent observations, categorized according to three schemes with two categories in each scheme, have been taken, it is customary to summarize the data in a 2 x 2 x 2 contingency table (...)

In this paper we consider an exploratory canonical analysis approach for multinomial population based on the $\phi$-divergence measure. We define the restricted minimum $\phi$-divergence estimator, which is seen to be a generalization of the restricted maximum likelihood estimator. This estimator is then used in $\phi$-divergence goodness-of-fit statistics which is the basis of two new families of statistics for solving the problem of selecting the number of significant correlations as well as the appropriateness...