On the moments of record values

In this paper some general relations for expectations of functions of record values are established. It is seen that these relations may be used to obtain recurrence relations for moments of record values. Bounds on expectations of record values with numerical computations are presented. Applications to the characterizations of the generalizeed exponential distribution are also given.     

More powerful modifications of unit root tests allowing structural change

It is well known that more powerful variants of Dickey–Fuller unit root tests are available. We apply two of these modifications, on the basis of simple maximum statistics and weighted symmetric estimation, to Perron tests allowing for structural change in trend of the additive outlier type. Local alternative asymptotic distributions of the modified test statistics are derived, and it is shown that their implementation can lead to appreciable finite sample and asymptotic gains in power over the standard tests. Also, these gains are largely comparable with those from GLS-based modifications to Perron tests, though some interesting differences do arise. This is the case for both exogenously and endogenously chosen break dates. For the latter choice, the new tests are applied to the Nelson–Plosser data.     

Some linear model techniques for analyzing small-circle spherical data

The author investigates least squares as a method for fitting small-circle models to a sample of unit vectors in R³. He highlights a local linear model underlying the estimation of the parameters of a circle. This model is used to construct an estimation algorithm and regression-type inference procedures for the parameters of a circle. It makes it possible to compare the fit of a small circle with that of a spherical ellipse. The limitations of the least-squares approach are emphasized: when the errors are bounded away from 0, the least-squares estimators are not consistent as the sample size goes to infinity. Two examples, concerned with the migration of elephant seals and with the classification of geological folds, are analyzed using the linear model techniques proposed in this work.     

Characterization of a class cf discrete distributions by properties of their moment distributions

The concept of a moment distribution is here applied to the class of factorial series distributions introduced by the author (197U). Moment distributions turn out to have a simple interpretation in this case and often take on a simple form. A few examples are given to illustrate this fact     

A Comparison of Unit-Root Test Criteria

During the past 15 years, the ordinary least squares estimator and the corresponding pivotal statistic have been widely used for testing the unit-root hypothesis in autoregressive processes. Recently, several new criteria, based on maximum likelihood estimators and weighted symmetric estimators, have been proposed. In this article, we describe several different test criteria. Results from a Monte Carlo study that compares the power of the different criteria indicate that the new tests are more powerful against the stationary alternative. Of the procedures studied, the weighted symmetric estimator and the unconditional maximum likelihood estimator provide the most powerful tests against the stationary alternative. As an illustration, the weekly series of one-month treasury-bill rates is analyzed.     

On comparing two poisson intensity functions

Given realizations of two possion processes with unknown intensities A(·) and F(·) observed over the interval (t₁,t₂), we suppose that it is desired to distinution between H₀ Ξ(·)/λ(·) is constant on (t₁,t₂) versus H₊:Ξ(·)/λ(·) increases on (t₁,t₂). We propose a decision rule which uses the percentage points of the Mann-Whitney U-distribution. We show that the decision rule is unbiased and that the set of alternatives in H₊ can be weakly ordered, specifically: if Ξ(·)/λ(·), β(·)/λ(·) and Ξ(·)/β(·) are increasing on (t₁, t₂) then P{H₀ is rejected |Ξ(·)}≧P{H₀ is rejected|B(·)}≧P{H₀ is rejected|H₀}.     

Estimation of the mean of a spherically symmetric distribution with constraints on the norm

The authors consider the problem of estimating, under quadratic loss, the mean of a spherically symmetric distribution when its norm is supposed to be known and when a residual vector is available. They give a necessary and sufficient condition for the optimal James‐Stein estimator to dominate the usual estimator. Various examples are given that are not necessarily variance mixtures of normal distributions. Consideration is also given to an alternative class of robust James‐Stein type estimators that take into account the residual vector. A more general domination condition is given for this class.     

Estimation of mean based on modified robust extreme ranked set sampling

In this paper, double robust extreme ranked set sampling (DRERSS) and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DRERSS gives unbiased estimators of the population mean. Also, it is found that DRERSS is more efficient than the simple random sampling (SRS), ranked set sampling (RSS), and extreme ranked set sampling (ERSS) methods. For asymmetric distributions considered in this study, the DRERSS has a small bias and it is more efficient than SRS, RSS, and ERSS. A real data set is used to illustrate the DRERSS method.     

Statistical inference on the drift parameter in fractional Brownian motion with a deterministic drift

In statistical inference on the drift parameter a in the fractional Brownian motion W^H_t with the Hurst parameter H ∈ (0, 1) with a constant drift Y^H_t = at + W^H_t, there is a large number of options how to do it. We may, for example, base this inference on the properties of the standard normal distribution applied to the differences between the observed values of the process at discrete times. Although such methods are very simple, it turns out that more appropriate is to use inverse methods. Such methods can be generalized to non constant drift. For the hypotheses testing about the drift parameter a, it is more proper to standardize the observed process, and to use inverse methods based on the first exit time of the observed process of a pre-specified interval until some given time. These procedures are illustrated, and their times of decision are compared against the direct approach. Other generalizations are possible when the random part is a symmetric stochastic integral of a known, deterministic function with respect to fractional Brownian motion.     

语篇象似性与语篇连贯

象似性存在于语言的各个层面上。在篇章层面上,象似性有着重要的语篇连贯功能,因为象似性是语篇视角在语篇构建时的具体体现。文章主要从声音象似性、视觉象似性、顺序象似性、对称象似性以及隐喻象似性来讨论语篇象似性和语篇连贯的关系。