Adaptive choice of scale tests in flexible two-stage designs with applications in experimental ecology and clinical trials

In this paper, the two-sample scale problem is addressed within the rank framework which does not require to specify the underlying continuous distribution. However, since the power of a rank test depends on the underlying distribution, it would be very useful for the researcher to have some information on it in order to use the possibly most suitable test. A two-stage adaptive design is used with adaptive tests where the data from the first stage are used to compute a selector statistic to select the test statistic for stage 2. More precisely, an adaptive scale test due to Hall and Padmanabhan and its components are considered in one-stage and several adaptive and non-adaptive two-stage procedures. A simulation study shows that the two-stage test with the adaptive choice in the second stage and with Liptak combination, when it is not more powerful than the corresponding one-stage test, shows, however, a quite similar power behavior. The test procedures are illustrated using two ecological applications and a clinical trial.     

Nonparametric measures of intraclass correlation

Three nonparametric measures of intraclass correlation based on the notion of concordance are considered. Their unbiased estimators and nonparametric tests based on the estimators are studied and it is shown that an analogue of the Kendall's tau provides small variance estimator and relatively powerful test. Furthermore, the approximate variance of the estimator is given when the correlation is small in the normal model.     

Polynomially solvable cases of the constant rank unconstrained quadratic 0-1 programming problem

In this paper we consider the constant rank unconstrained quadratic 0-1 optimization problem, CR-QP01 for short. This problem consists in minimizing the quadratic function 〈x, Ax〉 + 〈c, x〉 over the set {0,1} ⁿ where c is a vector in ℝ ⁿ and A is a symmetric real n × n matrix of constant rank r. We first present a pseudo-polynomial algorithm for solving the problem CR-QP01, which is known to be NP-hard already for r = 1. We then derive two new classes of special cases of the CR-QP01 which can be solved in polynomial time. These classes result from further restrictions on the matrix A. Finally we compare our algorithm with the algorithm of Allemand et al. (2001) for the CR-QP01 with negative semidefinite A and extend the range of applicability of the latter algorithm. It turns out that neither of the two algorithms dominates the other with respect to the class of instances which can be solved in polynomial time.     

矩阵秩的等式若干讨论

矩阵的秩是矩阵的重要数字特征之一,文章从矩阵秩的定义出发,给出了矩阵秩的若干等式.     

Nonparametric multiple comparison procedures for unbalanced two-way layouts

In this paper, we consider nonparametric multiple comparison procedures for unbalanced two-way factorial designs under a pure nonparametric framework. For multiple comparisons of treatments versus a control concerning the main effects or the simple factor effects, the limiting distribution of the associated rank statistics is proven to satisfy the multivariate totally positive of order two condition. Hence, asymptotically the proposed Hochberg procedure strongly controls the familywise type I error rate for the simultaneous testing of the individual hypotheses. In addition, we propose to employ Shaffer's modified version of Holm's stepdown procedure to perform simultaneous tests on all pairwise comparisons regarding the main or simple factor effects and to perform simultaneous tests on all interaction effects. The logical constraints in the corresponding hypothesis families are utilized to sharpen the rejective thresholds and improve the power of the tests.     

On the natural restrictions in the singular Gauss–Markov model

A Gauss–Markov model is said to be singular if the covariance matrix of the observable random vector in the model is singular. In such a case, there exist some natural restrictions associated with the observable random vector and the unknown parameter vector in the model. In this paper, we derive through the matrix rank method a necessary and sufficient condition for a vector of parametric functions to be estimable, and necessary and sufficient conditions for a linear estimator to be unbiased in the singular Gauss–Markov model. In addition, we give some necessary and sufficient conditions for the ordinary least-square estimator (OLSE) and the best linear unbiased estimator (BLUE) under the model to satisfy the natural restrictions.      

明茨洛夫会见过的三位唐努乌梁海上层人物

1914年,俄国官员明茨洛夫前往唐努乌梁海进行侦察活动,为沙俄吞并唐努乌梁海作准备.明茨洛夫此行分别会见了萨拉吉克旗总管、克穆齐克旗总管及克旗堪布大喇嘛.本文考述了这三位唐努乌梁海上层人物的情况.     

基于Copula函数的金融市场尾部相关性分析

在常规极大似然估计法中，Copula函数的参数估计受边缘分布函数拟和的影响较大，鉴于此，用基于秩的极大似然法估计Copula函数的参数，并结合常见的4类双参数非对称BBx—Copula函数，对民生银行和浦发银行这两只股票的尾部相关性进行实证分析，结果表明股票市场在低迷时期的尾部相关性高于活跃时期的尾部相关性。     

Model selection criteria for reduced rank multivariate time series: a simulation study

The main focus of our paper is to compare the performance of different model selection criteria used for multivariate reduced rank time series. We consider one of the most commonly used reduced rank model, that is, the reduced rank vector autoregression (RRVAR (p, r)) introduced by Velu et al. [Reduced rank models for multiple time series. Biometrika. 1986;7(31):105–118]. In our study, the most popular model selection criteria are included. The criteria are divided into two groups, that is, simultaneous selection and two-step selection criteria, accordingly. Methods from the former group select both an autoregressive order p and a rank r simultaneously, while in the case of two-step criteria, first an optimal order p is chosen (using model selection criteria intended for the unrestricted VAR model) and then an optimal rank r of coefficient matrices is selected (e.g. by means of sequential testing). Considered model selection criteria include well-known information criteria (such as Akaike information criterion, Schwarz criterion, Hannan–Quinn criterion, etc.) as well as widely used sequential tests (e.g. the Bartlett test) and the bootstrap method. An extensive simulation study is carried out in order to investigate the efficiency of all model selection criteria included in our study. The analysis takes into account 34 methods, including 6 simultaneous methods and 28 two-step approaches, accordingly. In order to carefully analyse how different factors affect performance of model selection criteria, we consider over 150 simulation settings. In particular, we investigate the influence of the following factors: time series dimension, different covariance structure, different level of correlation among components and different level of noise (variance). Moreover, we analyse the prediction accuracy concerned with the application of the RRVAR model and compare it with results obtained for the unrestricted vector autoregression. In this paper, we also present a real data application of model selection criteria for the RRVAR model using the Polish macroeconomic time series data observed in the period 1997–2007.     

Estimation of cointegrated models with exogenous variables

We consider a cointegrated vector autoregressive process of integrated order 1, where the process consists of endogenous variables and exogenous variables. Johansen [Cointegration in partial systems and the efficiency of single-equation analysis. J Econometrics. 1992;52:389–402], Harbo et al. [Asymptotic inference on cointegrating rank in partial systems. J Amer Statist Assoc. 1998;16:388–399], and Pesaran et al. [Structural analysis of vector error correction models with exogenous I(1) variables. J Econometrics. 2000;97:293–343] considered inference of such processes assuming that the non-stationary exogenous variables are not cointegrated, and thus they are weakly exogenous. We consider the case where exogenous variables are cointegrated. Parameterization and estimation of the model is considered, and the asymptotic properties of the estimators are presented. The method in this paper is also applicable for the models considered in Mosconi and Giannini [Non-causality in cointegrated systems: representation estimation and testing. Oxford Bull Econ Stat. 1992;54:399–417], Pradel and Rault [Exogeneity in vector error correction models with purely exogenous long-run paths. Oxford Bull Econ Stat. 2003;65:629–653], and Hunter [Cointegrating exogeneity. Econom Lett. 1990;34:33–35]. A real data example is provided to illustrate the methods. Finite sample properties of the estimators are also examined through a Monte Carlo simulation.