Dependence Estimation for High‐frequency Sampled Multivariate CARMA Models

The paper considers high‐frequency sampled multivariate continuous‐time autoregressive moving average (MCARMA) models and derives the asymptotic behaviour of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behaviour of the cross‐covariances between different components of the model. We will see that the limit distribution of the sample autocovariance function has a similar structure in the continuous‐time and in the discrete‐time model. As a special case, we consider a CARMA (one‐dimensional MCARMA) process. For a CARMA process, we prove Bartlett's formula for the sample autocorrelation function. Bartlett's formula has the same form in both models; only the sums in the discrete‐time model are exchanged by integrals in the continuous‐time model. Finally, we present limit results for multivariate MA processes as well, which are not known in this generality in the multivariate setting yet.     

Markov-modulated infinite-server queues driven by a common background process

This paper studies a system with multiple infinite-server queues that are modulated by a common background process. If this background process, being modeled as a finite-state continuous-time Markov chain, is in state j, then the arrival rate into the i-th queue is λ_{i, j}, whereas the service times of customers present in this queue are exponentially distributed with mean μ^{? 1}_{i, j}; at each of the individual queues all customers present are served in parallel (thus reflecting their infinite-server nature).

Three types of results are presented: in the first place (i) we derive differential equations for the probability-generating functions corresponding to the distributions of the transient and stationary numbers of customers (jointly in all queues), then (ii) we set up recursions for the (joint) moments, and finally (iii) we establish a central limit theorem in the asymptotic regime in which the arrival rates as well as the transition rates of the background process are simultaneously growing large.     

Optimum Mixture Design for the Detection of Synergistic Effects

In mixture experiments, optimal designs for the estimation of parameters, both linear and non-linear, have been discussed by several authors. Optimal designs for the estimation of a subset of parameters have also been investigated. However, designs for testing the effects of certain factors and interactions have been studied only in the context of response surface models. In this article, we attempt to find the optimum design for testing the presence of synergistic effects in a mixture model. The classical F-test has been considered and the optimum design has been obtained so as to maximize the power of the test. It is observed that the barycenters are necessarily the support points of the trace-optimal design.     

Allocating observations in a test for the ratio of scales of independent gamma variates

Consider two independent gamma populations with common shape parameter α. Let ρ denote the ratio of their scale parameters, and consider the problem of testing the null hypothesis ρ = 1 against the alternative ρ = 1 + r , where r >0 . A procedure, not depending on α , that maximizes the exact slope at this alternative is proposed.     

Conditionally gaussian distributions and an application to kalman filtering with stochastic regressors

The work reviews theory of conditionally Gaussian distributions, especially so called theorems on normal correlation. Three theorems are given: the basic, the recursive, and the conditional theorem on normal correlation. They assume that (a,y), (a,x,y), or (a,y,z) has a Gaussian distribution, ussert that (a,y), (a,x,y), and (a,y,z), respectively, are Gaussian, and give formulas for the corresponding conditional mean vectors and variance covariance matrices. A proof is presented for the recursive and the conditional theorem.     

Nonparametric validation of similar distributions and assessment of goodness of fit

In this paper the problem of assessing the similarity of two cumulative distribution functions F and G is considered. An asymptotic test based on an α-trimmed version of Mallows distance Γ_α( F , G ) between F and G is suggested, thus demonstrating the similarity of F and G within a preassigned Γ_α( F , G ) neighbourhood at a controlled type I error rate. The test proposed is applied to the validation of goodness of fit and for the nonparametric assessment of bioequivalence. It is shown that Γ_α( F , G ) can be interpreted as average and population equivalence. Our approach is illustrated by various examples.     

用不动点定理研究方程解的存在性

介绍常用的不动点定理,并给出它在方程中有关解的存在问题的应用实例.     

论中国古诗英译中的语音形式偏移

以等效翻译理论为依据,采用理论和译文分析相结合的方式论证了中国古诗英译中语音形式偏移这一翻译变通手段.从而指出,为忠实传达原作的效果,语音形式偏移在中国古诗英译中是不可避免的,甚至是必要的.     

ON THE NUMBER OF RECORDS NEAR THE MAXIMUM

Recent work has considered properties of the number of observations X_j, independently drawn from a discrete law, which equal the sample maximum X_(n) The natural analogue for continuous laws is the number K_n(a) of observations in the interval (X_(n)–a, X_(n)], where a > 0. This paper derives general expressions for the law, first moment, and probability generating function of K_n(a), mentioning examples where evaluations can be given. It seeks limit laws for n→ and finds a central limit result when a is fixed and the population law has a finite right extremity. Whenever the population law is attracted to an extremal law, a limit theorem can be found by letting a depend on n in an appropriate manner; thus the limit law is geometric when the extremal law is the Gumbel type. With these results, the paper obtains limit laws for ‘top end’ spacings X_(n) - X_(n-j) with j fixed.     

Parameter Neutral Optimum Design for Non-linear Models

Some Bayesian approaches to D -optimum design of experiments are considered from the viewpoint of invariance under reparameterization of the underlying statistical model. An invariant criterion is proposed which does not require the detailed specification of a prior, and which is shown to be equivalent to G -optimality under a Jeffreys prior. The methods are applied and discussed in the contexts of exponential decay and quantal response models.