On approximate likelihood inference in a poisson mixed model

A two-step estimation approach is proposed for the fixed-effect parameters, random effects and their variance σ² of a Poisson mixed model. In the first step, it is proposed to construct a small σ²-based approximate likelihood function of the data and utilize this function to estimate the fixed-effect parameters and σ². In the second step, the random effects are estimated by minimizing their posterior mean squared error. Methods of Waclawiw and Liang (1993) based on so-called Stein-type estimating functions and of Breslow and Clayton (1993) based on penalized quasilikelihood are compared with the proposed likelihood method. The results of a simulation study on the performance of all three approaches are reported.     

Variable selection for multivariate generalized linear models

Generalized linear models (GLMs) are widely studied to deal with complex response variables. For the analysis of categorical dependent variables with more than two response categories, multivariate GLMs are presented to build the relationship between this polytomous response and a set of regressors. Traditional variable selection approaches have been proposed for the multivariate GLM with a canonical link function when the number of parameters is fixed in the literature. However, in many model selection problems, the number of parameters may be large and grow with the sample size. In this paper, we present a new selection criterion to the model with a diverging number of parameters. Under suitable conditions, the criterion is shown to be model selection consistent. A simulation study and a real data analysis are conducted to support theoretical findings.     

Asymptotic distributions in affiliation networks with an increasing sequence

A central limit theorem for a linear combination of all the maximum likelihood estimators with an increasing dimension for affiliation networks has been established. Simulation studies are provided to illustrate the asymptotic results.     

A general class of non parametric tests for comparing scale parameters

In this paper, a general class of non parametric tests is proposed for the two-sample scale problem. Testing of the scale parameter is very useful in real-life situations commonly faced in engineering, trade, cultivation, industries, medicine, etc. In all these fields, one will prefer the method that gives more consistent results. Thus, it is worthwhile to test the equality of scale parameters. The distribution of the proposed test is established. To assess the performance of the proposed test, the asymptotic efficacies are studied for some underlying distributions and the results are interpreted with useful information. To see the working of the proposed test, an illustrative example for the real-life data set is provided. The simulation study is also carried out to find the asymptotic power of the proposed test. An extension of the general class of tests to the multiple-sample problem is also discussed.     

A bivariate distribution with Lomax and geometric margins

We develop a stochastic model describing the joint distribution of $(X,N)$, where $N$ has a geometric distribution while $X$ is the sum of $N$ dependent, heavy-tail Pareto components. Models of this form arise in many applications, ranging from hydro-climatology to finance and insurance. We present fundamental properties of this vector, including marginal and conditional distributions, moments, representations, and parameter estimation. We also include an example from finance, illustrating modeling potential of this new bivariate distribution.     

SABR随机波动率LIBOR市场模型的参数校准估计方法与实证模拟

针对标准化Libor市场模型（LMM）和Heston随机波动率Libor市场模型（Heston-LMM）的应用局限,首先将SABR代替Heston过程引入标准化Libor市场模型框架,建立非标准化的SABR随机波动率Libor市场模型（SABR-LMM）;在此基础上,运用利率上限期权（Cap）、利率互换期权（Swaption）和自适应马尔科夫链蒙特卡罗模拟方法（MCMC）对模型参数进行有效市场校准与模拟估计;最后,针对三个月美元Libor远期利率实际数据,对上述三类Libor市场模型的实际运行效果进行了实证模拟计算与比较分析。研究结论认为,基于模拟利差计算结果,针对短期Libor利率模拟而言,与LMM和Heston -LMM两类模型而言,加入SABR波动项的SABR-LMM模型具有更小的模拟误差,因而具有更好的模拟效果。     

Approximate jackknife empirical likelihood method for estimating equations

It is known that the profile empirical likelihood method based on estimating equations is computationally intensive when the number of nuisance parameters is large. Recently, Li, Peng, & Qi (2011) proposed a jackknife empirical likelihood method for constructing confidence regions for the parameters of interest by estimating the nuisance parameters separately. However, when the estimators for the nuisance parameters have no explicit formula, the computation of the jackknife empirical likelihood method is still intensive. In this paper, an approximate jackknife empirical likelihood method is proposed to reduce the computation in the jackknife empirical likelihood method when the nuisance parameters cannot be estimated explicitly. A simulation study confirms the advantage of the new method. The Canadian Journal of Statistics 40: 110–123; 2012 © 2012 Statistical Society of Canada     

A new role for Low German? Language insertion as bilingual practice in the process of language shift

This article analyzes language insertion as a bilingual communicative practice, applying a functional, speaker‐focused approach to the study of sociolinguistics and language contact. The article is based on a study of contact phenomena in a formerly diglossic region in Northern Germany, where the previously spoken language – Low German – is in the process of being replaced by the dominant standard variety, German. It examines regional publications in order to establish the linguistic techniques by which Low German elements are incorporated into the Standard German texts and the communicative purposes that they serve. The paper concludes that in the process of language shift an emblematic repertoire from Low German is created which can be applied into the dominant contact language, German, for specific communicative purposes. Ausgehend von einer funktionalen, sprecherzentrierten soziolinguistischen Herangehensweise werden im folgenden Artikel bilinguale Einfügungen als Form mehrsprachiger kommunikativer Praxis untersucht. Die Studie analysiert Kontaktphänomene in einer vormals diglossischen Region Norddeutschlands, in der die gesprochene Sprache Niederdeutsch zunehmend von der dominanten Kontaktsprache Deutsch ersetzt wird. Im Artikel werden regionale Publikationen untersucht, um die sprachlichen Techniken heraus zu arbeiten, mit denen niederdeutsche Elemente in den Text integriert werden und welche kommunikativen Funktionen mit ihnen verbunden sind. Der Artikel kommt zu dem Ergebnis, dass während eines Prozesses von fortschreitendem Sprachverlust ein emblematisches niederdeutsches Repertoire geschaffen wird, das für spezifische Funktionen in die dominante Kontaktsprache Deutsch eingefügt werden kann. [Standard German] In disse Artikel geiht dat um Insprengsels van en Spraak in en anner. De Autor hett unnersöcht un lett weten, dat in Noorddüütskland as en tweetalerge Kuntrei immer mehr de sproken Spraak Nedderdüütsk van de machterge Kuntaktspraak Hoogdüütsk bisieddrückt un oflööst word. Se hett Schrifftstücken ut de Gewesten unnersöcht un deit wiesen, up wat för Maneren nedderdüütske Insprengsels in hoogdüütske Texten inbunnen worden. Daarbi kummt vandag, dat en egenaardig nedderdüütsk Weeswark upkummt, dat bi besünner Gelegenheiden in dat Hoogdüütsk sien Stee kriegen kann. [Low German]     

φ-混合序列的强大数律和收敛速度

用一般方法证明了φ-混合序列的强大数律、强收敛速度和随机变量上确界的可积性。