H-likelihood: problems and solutions

In recent issues of this journal it has been asserted in two papers that the use of h-likelihood is wrong, in the sense of giving unsatisfactory estimates of some parameters for binary data (Kuk and Cheng, 1999; Waddington and Thompson, 2004) or theoretically unsound (Kuk and Cheng, 1999). We wish to refute both these assertions.     

Law of iterated logarithm and almost sure limit points for random sums

Let {X_n,n≥1} be a sequence of independent identically distributed (i.i.d) random variables with a common distribution function F. When F belongs to the domain of partial attraction of a Semi-Stable law with index ,0<<2, we give complete solution to the results of R. Vasudeva and G. Divanji [Law of iterated logarithm for random subsequences, Statist. Probab. Lett. 12 (1991) 189–194], where they obtained Chover’s form of the law of iterated logarithm for random subsequences. Further, we extended the situation in obtaining almost sure limit points for random subsequences.     

Estimation for hidden Markov random fields

A finite state Markov random field is noisily observed via a second finite state process. The parameters of the model are estimated, as well as the most likely signal given the observations.     

燃烧诱发的炉墙结构振动

本文根据实测得到的国产300MW锅炉燃烧压力场功率谱密度函数,研究了用计算方法估计由燃烧诱发的结构振动,并与用实测方法获得的振动值作了对比,结果很接近。从而证明计算所用的数据与方法是可靠的。     

Saddlepoint approximations for some models of circular data

In this article we provide saddlepoint approximations for some important models of circular data. The particularity of these saddlepoint approximations is that they do not require solving the saddlepoint equation iteratively, so their evaluation is immediate. We first give very accurate approximations to P-values, critical values and power functions for some optimal tests regarding the concentration parameter under wrapped symmetric α-stable and circular normal models. Then, we consider an approximation to the distribution of a projection of the two-dimensional Pearson random walk with exponential step sizes.     

Using sibling data to understand the impact of family group decision-making on child welfare outcomes

Few studies have examined the impact of family group decision-making (FGDM) on child welfare outcomes. Studies in this area have often suffered from small sample sizes and lack of adequate comparison groups. Since FGDM is administered at the family level, sibling data provides an ideal way to compensate for small sample sizes and low enrollment rates in research evaluating FGDM. This study utilized sibling data from California's Title IV-E Waiver Demonstration Project Evaluation in Fresno and Riverside Counties to compare child welfare outcomes for children of families randomly assigned to receive FGDM (Fresno County, n = 110; Riverside County, n = 87) to children of families assigned to receive traditional child welfare services (Fresno County, n = 74; Riverside County, n = 52). After controlling for clustering effects using general estimating equations (GEE), group differences in child maltreatment, placement stability, and permanence were modeled using linear and logistic regression. Outcomes from both counties suggested no group differences. Though neutral outcomes on child welfare indicators may bring into question FGDM's efficacy for changing child welfare outcomes, this study confirms previous findings with smaller sample sizes on the impact of FGDM and demonstrates a methodological improvement over individual or family-case analyses.     

Likelihood Estimation for Censored Random Vectors

This article shows how to construct a likelihood for a general class of censoring problems. This likelihood is proven to be valid, i.e. its maximizer is consistent and the respective root-n estimator is asymptotically efficient and normally distributed under regularity conditions. The method generalizes ordinary maximum likelihood estimation as well as several standard estimators for censoring problems (e.g. tobit type I-tobit type V).     

Model and design correspondence in finite population sampling

A correspondence rule is suggested for the choice of a sampling design when prior knowledge concerning a finite population is available. Designs satisfying the correspondence rule are discussed in the case of random permutations models. A general optimality theorem is given for strategies under such models. Approximate correspondences satisfied by systematic sampling and πps sampling are also indicated.     

On random variate generation for the generalized hyperbolic secant distributions

We give random variate generators for the generalized hyperbolic secant distribution and related families such as Morris's skewed generalized hyperbolic secant family and a family introduced by Laha and Lukacs. The rejection method generators are uniformly fast over the parameter space and are based upon a complex function representation of the distributions due to Harkness and HarknessThe author's research was sponsored by NSERC Grant A3456 and FCAR Grant 90-ER-0291.     

A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

In a previous paper the authors proposed a simple method to extend results about almost sure convergence for weighted sums of real random variables to the case of Banach-valued random elements. The method arises from the extension of Skorohod's Representation Theorem for weakly convergent sequences due to Blackwell and Dubins, applied to the general framework of weakly equivalent tight sequences of probability measures. This provides a scheme which permits us to handle separately a problem that behaves like the Glivenko-Cantelli Theorem and a question on uniform integrability which generally is reduced to the real valued version of the general problem to be solved.

In this paper we prove that Wasserstein's metrics can play the same role as Skorohod's Representation Theorem in the preceding scheme. We also show that our method can be applied to obtain results with respect to various summability methods (Abel, Euler, …) even in the case in which the ‘weights’ are linear operators.