A pseudo restricted MLE under multivariate order restrictions and its algorithm

Abstract

It is shown in this paper that a quasi order for the vectors in R^p is a cone induced if and only if the order is preservable under limits and under linear combinations with non-negative coefficients. For the mean vectors in MANOVA subject to the restriction of simple ordering, a pseudo restricted MLE is proposed. This estimator is a matrix projection onto a closed convex set inside the restricted domain. An algorithm for the pseudo restricted MLE is developed, that computes the matrix projections using only vector projections.     

Some new results on univariate and multivariate permutation tests for ordinal categorical variables under restricted alternatives

In several sciences, especially when dealing with performance evaluation, complex testing problems may arise due in particular to the presence of multidimensional categorical data. In such cases the application of nonparametric methods can represent a reasonable approach. In this paper, we consider the problem of testing whether a “treatment” is stochastically larger than a “control” when univariate and multivariate ordinal categorical data are present. We propose a solution based on the nonparametric combination of dependent permutation tests (Pesarin in Multivariate permutation test with application to biostatistics. Wiley, Chichester, 2001), on variable transformation, and on tests on moments. The solution requires the transformation of categorical response variables into numeric variables and the breaking up of the original problem’s hypotheses into partial sub-hypotheses regarding the moments of the transformed variables. This type of problem is considered to be almost impossible to analyze within likelihood ratio tests, especially in the multivariate case (Wang in J Am Stat Assoc 91:1676–1683, 1996). A comparative simulation study is also presented along with an application example.     

Modifications of the Mack-Wolfe umbrella tests for a generalized Behrens-Fisher problem

We are concerned with testing procedures for umbrella alternatives in the k-sample location problem without making the assumption that the underlying populations have the same shape. Modifications of the Mack-Wolfe tests are proposed for the cases when the peak of the umbrella is known or unknown. The proposed procedures are exactly distribution-free when the continuous populations have the same shape. The modified test for peak-known umbrella alternatives remains asymptotically distribution-free when the continuous populations are symmetric, but not necessarily with the same shape.     

论蒙古族聚居区县域经济发展的路径选择——以阿鲁科尔沁旗为例

以阿鲁科尔沁旗为例,分析蒙古族聚居区县域经济基本特征;从生态环境、基础设施条件、资金及教育等方面入手,阐述制约蒙古族聚居区县域经济发展的主要因素;提出蒙古族聚居区县域经济发展的路径选择,打造蒙古族聚居区县城经济发展的基础。     

Double hierarchical generalized linear models (with discussion)

Summary.  We propose a class of double hierarchical generalized linear models in which random effects can be specified for both the mean and dispersion. Heteroscedasticity between clusters can be modelled by introducing random effects in the dispersion model, as is heterogeneity between clusters in the mean model. This class will, among other things, enable models with heavy-tailed distributions to be explored, providing robust estimation against outliers. The h -likelihood provides a unified framework for this new class of models and gives a single algorithm for fitting all members of the class. This algorithm does not require quadrature or prior probabilities.     

Optimal block sequences for blocked fractional factorial split-plot designs

It is known that for blocked 2^n-k$2^{n-k}$ designs a judicious sequencing of blocks may allow one to obtain early and insightful results regarding influential parameters in the experiment. Such findings may justify the early termination of the experiment thereby producing cost and time savings. This paper introduces an approach for selecting the optimal sequence of blocks for regular two-level blocked fractional factorial split-plot screening experiments. An optimality criterion is developed so as to give priority to the early estimation of low-order factorial effects. This criterion is then applied to the minimum aberration blocked fractional factorial split-plot designs tabled in McLeod and Brewster [2004. The design of blocked fractional factorial split-plot experiments. Technometrics 46, 135–146]. We provide a catalog of optimal block sequences for 16 and 32-run minimum aberration blocked fractional factorial split-plot designs run in either 4 or 8 blocks.     

Comparing Sub-Survival Functions in a Competing Risks Model

In the competing risks literature, one usually compares whether two risks are equal or whether one is more serious. In this paper, we propose tests for the equality of two competing risks against an ordered alternative specified by their sub-survival functions. These tests are naturally developed as extensions of those based on hazard rates and cumulative incidence functions. We note that the interpretation of the new test results is more direct compared to the situation when the hypotheses are framed in terms of their cumulative incidence functions. The proposed tests are of the Kolmogrov–Smirnov type, based on maximum differences between sub-survival functions. Our simulation studies indicate that they are excellent competitors of the existing tests, that are based mainly on differences between cumulative incidence functions. A numerical example will demonstrate the advantages of the proposed tests.     

The two-sample problem with multivariate censored data: a new rank test family

A new rank test family is proposed to test the equality of two multivariate failure times distributions with censored observations. The tests are very simple: they are based on a transformation of the multivariate rank vectors to a univariate rank score and the resulting statistics belong to the familiar class of the weighted logrank test statistics. The new procedure is also applicable to multivariate observations in general, such as repeated measures, some of which may be missing. To investigate the performance of the proposed tests, a simulation study was conducted with bivariate exponential models for various censoring rates. The size and power of these tests against Lehmann alternatives were compared to the size and power of two other tests (Wei and Lachin, 1984 and Wei and Knuiman, 1987). In all simulations the new procedures provide a relatively good power and an accurate control over the size of the test. A real example from the National Cooperative Gallstone Study is given     

A Note on Testing Homogeneity of Several Exponential Location Parameters

In this article, the problems of testing homogeneity of several exponential location parameters against simple and tree ordered alternatives are considered separately. Test procedures for both the alternatives are proposed using restricted maximum likelihood estimators (RMLE) of exponential location parameters under the respective orderings. Critical constants for the implementation of the proposed procedures are tabulated. Power comparison of the proposed test procedure under the simple ordered alternative with the procedure of Chen (1982 Chen , H. J. ( 1982 ). A new range statistic for comparisons of several exponential location parameters . Biometrika 69 ( 1 ): 257 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]) and of Dhawan and Gill (1999 Dhawan , A. K. , Gill , A. N. ( 1999 ). A one-sided test for testing homogeneity of scale parameters against ordered alternative . Communication in Statistics—Theory and Methods 28 ( 10 ): 2417 – 2439 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is carried out using Monte-Carlo simulation.     

Locally Most Powerful Rank Tests for Comparison of Two Failure Rates Based on Multiple Type-II Censored Data

This article deals with the locally most powerful rank tests for testing the hypothesis that two failure rates are equal against the alternative that one failure rate is greater than the other, when the combined ordered sample is multiple Type-II censored. A modified version of the Dupa? and Hájek (1969 Dupa? , V. , Hájek , J. (1969). Asymptotic normality of simple linear rank statistics under alternatives II. Ann. Math. Statist. 40:1992–2017.[Crossref] , [Google Scholar]) theorem is used to establish their asymptotic normality under fixed alternative since the scores generating functions associated with these rank test statistics have a finite number of jump discontinuities. The modified version that leads to a simpler centering constant, is proved by Dupa? (1970 Dupa? , V. ( 1970 ). A contribution to the asymptotic normality of simple linear rank statistics. In: Puri, M. L., ed. Nonparametric Techniques in Statistical Inference. Cambridge: Cambridge University Press . [Google Scholar]) using the results of Hájek (1968 Hájek , J. ( 1968 ). Asymptotic normality of simple linear rank statistics under alternatives . Ann. Math. Statist. 39 : 325 – 346 .[Crossref] , [Google Scholar]). The Pitman AREs of these rank tests based on censored data relative to the corresponding tests based on complete data are obtained under some Lehmann-type alternative distributions such that their failure rates dominate the failure rates of the respective null distributions. The AREs are computed numerically for single (left or right) and double censored data, and the extent of loss due to these censoring schemes is discussed. The rank tests considered here include among them the Mann-Whiney-Wilcoxon (MWW) test, the Savage test, and the linear combination of these two tests. In the case of all the tests, except the MWW test, it is found that the loss of efficiency due to left censoring is considerably less than that due to right censoring. In the case of finite samples, Monte Carlo simulation results showing the empirical levels and empirical powers against some Lehmann alternatives are presented.