A Statistical analysis of spatial point patterns A case study

In the project "statistical image analysis" of CWI we have studied some spatial point patterns that originated from biological observations. These observations were the positions of so called EGF-receptors on the surface of human carcinoma cells.
We propose a stochastic model for these point patterns. Since the EGF-receptors appear in clusters on the cell surface, we have opted for the Poisson-cluster-process as the model. We estimated the three parameters in this process by means of a method described by Diggle. We also did some work in assessing the statistical reliability of our estimates.     

Generalized runs tests for the IID hypothesis

We provide a family of tests for the IID hypothesis based on generalized runs, powerful against unspecified alternatives, providing a useful complement to tests designed for specific alternatives, such as serial correlation, GARCH, or structural breaks. Our tests have appealing computational simplicity in that they do not require kernel density estimation, with the associated challenge of bandwidth selection. Simulations show levels close to nominal asymptotic levels. Our tests have power against both dependent and heterogeneous alternatives, as both theory and simulations demonstrate.     

Improving the J Test in the SARAR Model by Likelihood-based Estimation

Abstract

It has been demonstrated recently that in small-to-medium samples the empirical significance levels of the asymptotic J-type tests for the SARAR model introduced by Kelejian (2008) can be controlled in many cases by the use of a bootstrap to construct a reference distribution. A feature of the popular GMM estimator in this context that deserves to receive more attention is that in small samples it will often deliver spatial parameter estimates that lie outside the invertibility region of the model. Using such illegitimate estimates to construct bootstrap samples is then problematic; the present paper finds that this practical obstacle may be removed by the use of quasi-maximum likelihood estimates that guarantee invertibility. The effects of different spatial weight patterns and sample size on the empirical significance levels and power of the tests are illustrated, and the paper demonstrates that estimation using QMLE, allied to a simple bootstrap, yields tests with reliable significance levels and reasonable power, in a majority of cases.

RÉSUMÉ dans des échantillons petits à moyens, il est possible, dans de nombreux cas, de contrôler les niveaux à signification empirique des tests asymptotiques introduits par Kelejian (2008) à l'aide d'un ‘bootstrap’. Dans ce contexte, une caractéristique de l'estimateur GMM, très répandu, est qu'il fournit, dans de petits échantillons, des estimations de paramètres spatiaux situés hors de la région d'inversibilité du modèle. L'emploi de telles estimations illégitimes pour la réalisation d’échantillons ‘bootstrap’ devient alors problématique; la présente communication indique que l'on peut supprimer cet obstacle pratique en utilisant le QMLE garantissant l'inversibilité. Les effets des tendances du poids spatial et la taille des échantillons sur les niveaux d'importance et la puissance sont illustrés, et la communication démontre que le QMLE, allié à un simple ‘bootstrap’, permet de réaliser des tests offrant, dans la plupart des vas, des niveaux d'importance fiables et une puissance raisonnable.

EXTRACTO En muestras entre pequeñas y medianas, los niveles de significancia empírica de las pruebas asintóticas de tipo J para el modelo SARAR introducidas por Kelejian (2008) pueden controlarse en muchos casos mediante el uso de un bootstrap. Una característica del popular estimador GMM dentro de este contexto es que en las muestras pequeñas, a menudo producirá estimaciones de parámetros espaciales que están fuera de la región de reversibilidad del modelo. No obstante, el empleo de este tipo de estimaciones ilegítimas para construir muestras bootstrap es problemático; el estudio actual muestra que este obstáculo práctico puede eliminarse mediante el uso del QMLE que garantiza la reversibilidad. Se ilustran los efectos de las pautas de peso espacial y del tamaño de la muestra sobre el poder y los niveles de significancia, y el estudio demuestra que el QMLE, aliado a un bootstrap simple, dota a las pruebas de niveles de significancia fiables y de un poder razonable, en la mayoría de los casos.

     

Testing for random effects in panel models with spatially correlated disturbances

In the empirical analysis of panel data the Breusch–Pagan (BP) statistic has become a standard tool to infer on unobserved heterogeneity over the cross-section. Put differently, the test statistic is central to discriminate between the pooled regression and the random effects model. Conditional versions of the test statistic have been provided to immunize inference on unobserved heterogeneity against random time effects or patterns of spatial error correlation. Panel data models with spatially correlated error terms are typically set out under the presumption of some known adjacency matrix parameterizing the correlation structure up to a scaling factor. This paper delivers a bootstrap scheme to generate critical values for the BP statistic allowing robust inference under misspecification of the adjacency matrix. Moreover, asymptotic results are derived for the case of a finite cross-section and infinite time dimension. Finite sample simulations show that misspecification of spatial covariance features could lead to large size distortions, while the robust bootstrap procedure retains asymptotic validity.     

Locally minimax test of independence in elliptically symmetrical distributions with additional observations

Summary LetX=(X _ij )=(X ₁, ...,X _n )’,X’ _i =(X _i1, ...,X _ip )’,i=1,2, ...,n be a matrix having a multivariate elliptical distribution depending on a convex functionq with parameters, 0,σ. Let ϱ²=ϱ ₂ ^-2 be the squared multiple correlation coefficient between the first and the remainingp ₂+p ₃=p−1 components of eachX _i . We have considered here the problem of testingH ₀:ϱ²=0 against the alternativesH ₁:ϱ ₁ ^-2 =0, ϱ ₂ ^-2 >0 on the basis ofX andn ₁ additional observationsY ₁ (n ₁×1) on the first component,n ₂ observationsY ₂(n ₂×p ₂) on the followingp ₂ components andn ₃ additional observationsY ₃(n ₃×p ₃) on the lastp ₃ components and we have derived here the locally minimax test ofH ₀ againstH ₁ when ϱ ₂ ^-2 →0 for a givenq. This test, in general, depends on the choice ofq of the familyQ of elliptically symmetrical distributions and it is not optimality robust forQ.     

Goodness-of-fit tests for discrete models based on the integrated distribution function

This paper presents a new widely applicable omnibus test for discrete distributions which is based on the difference between the integrated distribution function Ψ(t)=∫_t ^∞ (1−F(x))dx and its empirical counterpart. A bootstrap version of the test for common lattice models has accurate error rates even for small samples and exhibits high power with respect to competitive procedures over a large range of alternatives. Received: July 1998     

Bootstrapping cointegrating regressions

The paper investigates the usefulness of bootstrap methods for small sample inference in cointegrating regression models. It discusses the standard bootstrap, the recursive bootstrap, the moving block bootstrap and the stationary bootstrap methods. Some guidelines for bootstrap data generation and test statistics to consider are provided and some simulation evidence presented suggests that the bootstrap methods, when properly implemented, can provide significant improvement over asymptotic inference.     

针对儿童的电梯安全警示标识系统的研究

在中国2～12岁儿童中,绝大多数儿童安全意识淡薄,对生活中可能出现的危险缺少应有的防范知识。儿童不能单独乘电梯,这已成为社会共识。但是在现实生活中,很少有人关注和研究与儿童安全乘电梯有关的警示标示图片系统的研究。文章在介绍了目前国内现行的电梯安全乘用警示标示图片的使用情况的基础上,从研究电梯安全警示标识的对象、内容、方式和强度入手,总结了针对儿童的电梯安全警示标示的文字、图形和色彩设计原则,并分别提供了针对垂直乘客电梯层门警示标识的参考图样和针对自动扶梯／移动走道安全警示标识的参考图样。     

Distributional inference

The making of statistical inferences in distributional form is conceptionally complicated because the epistemic 'probabilities' assigned are mixtures of fact and fiction. In this respect they are essentially different from 'physical' or 'frequency-theoretic' probabilities. The distributional form is so attractive and useful, however, that it should be pursued. Our approach is In line with Walds theory of statistical decision functions and with Lehmann's books about hypothesis testing and point estimation: loss functions are defined, risk functions are studied, unbiasedness and equivariance restrictions are made, etc. A central theme is that the loss function should be 'proper'. This fundamental concept has been explored by meteorologists, psychometrists, Bayesian statisticians, and others. The paper should be regarded as an attempt to reconcile various schools of statisticians. By accepting what we regard 88 good and useful in the various approaches we are trying to develop a nondogmatic approach.     

从民间工艺美术谈陕西区域性设计

陕西省是一个有着深厚文化底蕴的省份,经过上千年的历史风雨,陕西民间形成众多的民间工艺形式,这些形式业已经成为陕西文化的一部分,集中体现了陕西人的审美心理特点。笔者在分析陕西典型民间工艺的基础上,从民俗文化、造型特征、色彩应用三个方面出发,概括出陕西"本土语言符号"的特点,并以此出发展开对陕西的区域性设计的分析。     

在公共场所设置手语服务窗口的可行性探究

随着我国城市化建设的不断进步和完善,城市公共场所也在一定程度上满足了广大人民群众在生活中休闲娱乐的要求。目前,城市公共场所在为聋哑人设置手语服务窗口这一举措未得到普及,使得聋哑群体在公共场所获取信息时存在一定的障碍。论文首先阐述了公共场所设置手语服务窗口的必要性,其次分析了在城市公共服务场所设置手语窗口的现状,最后为公共场所设置手语服务窗口提供了解决方案。     

Bootstrap unit root tests in panels with cross-sectional dependency

We apply bootstrap methodology to unit root tests for dependent panels with N cross-sectional units and T time series observations. More specifically, we let each panel be driven by a general linear process which may be different across cross-sectional units, and approximate it by a finite order autoregressive integrated process of order increasing with T. As we allow the dependency among the innovations generating the individual series, we construct our unit root tests from the estimation of the system of the entire N cross-sectional units. The limit distributions of the tests are derived by passing T to infinity, with N fixed. We then apply bootstrap method to the approximated autoregressions to obtain critical values for the panel unit root tests, and establish the asymptotic validity of such bootstrap panel unit root tests under general conditions. The proposed bootstrap tests are indeed quite general covering a wide class of panel models. They in particular allow for very general dynamic structures which may vary across individual units, and more importantly for the presence of arbitrary cross-sectional dependency. The finite sample performance of the bootstrap tests is examined via simulations, and compared to that of commonly used panel unit root tests. We find that our bootstrap tests perform relatively well, especially when N is small.     

Bootstrap refinements for QML estimators of the GARCH(1,1) parameters

This paper reconsiders a block bootstrap procedure for Quasi Maximum Likelihood estimation of GARCH models, based on the resampling of the likelihood function, as proposed by Gonçalves and White [2004. Maximum likelihood and the bootstrap for nonlinear dynamic models. Journal of Econometrics 119, 199–219]. First, we provide necessary conditions and sufficient conditions, in terms of moments of the innovation process, for the existence of the Edgeworth expansion of the GARCH(1,1) estimator, up to the k$k$-th term. Second, we provide sufficient conditions for higher order refinements for equally tailed and symmetric test statistics. In particular, the bootstrap estimator based on resampling the likelihood has the same higher order improvements in terms of error in the rejection probabilities as those in Andrews [2002. Higher-order improvements of a computationally attractive k$k$-step bootstrap for extremum estimators. Econometrica 70, 119–162].