Power comparisons between the F-test,the studentised range test,and an optimal test of the equality of several normal means

The power assessment of tests of the equality of k normal means such as the k treatment means in a one-way fixed effects analysis of variance model is addressed. Power assessment is considered in terms of a constraint on the range of the treatment means. The power properties of the standard F-test and Studentised range test are compared with those of an optimal (minimax) test procedure, which is known to maximise power levels under this constraint. It is shown that the standard test procedures compare well with the optimal test procedure, and in particular, the Studentised range test is shown to be practically as good as optimal in this setting.     

Unbiased tests for some one-sided testing problems

Unbiased tests are found for various testing problems. In the first model considered we test homogeneity of k + 1 independent one-parameter exponential family populations vs. the tree-top ordering alternative. The tree-top alternative is appropriate for one-sided comparisons for treatments with a control. In the next set of models normality is assumed. In one such model k independent populations have different unknown means but have an unknown common variance. An independent estimate of the variance exists. We test homogeneity of means against the alternative of no homogeneity. We also consider the alternative of an ordering of the means as well as the tree-top ordering. The final model considered is when we take a random sample from a multivariate normal population with unknown mean vector and an unknown covariance matrix of the intraclass type. We test the hypothesis that the mean vector is the zero vector against the one-sided alternative that each mean is nonnegative (with at least one positive).     

An Empirical Investigation of the “Dynamic McFadden” Model of Purchase Timing and Brand Choice: Implications for Market Structure

Purchase timing and brand-choice decisions of households are jointly investigated using the “dynamic McFadden” model of Heckman and Singer. The hazard of brand purchase is decomposed into the category purchase hazard and the probability of brand choice conditional on category purchase. The former is modeled using the hazard-function approach and the latter using a logit model. Unobserved heterogeneity in brand preferences, marketing effects, and baseline hazard parameters is accounted for in the empirical analysis. The distribution of preference heterogeneity identifies the locations of brands in multiattribute perceptual space and the distribution of attribute importance weights across households.     

A new nonlinear unit root test with Fourier function

Abstract

Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an exponential smooth threshold autoregressive (ESTAR) model. The simulation results indicate that the proposed unit root test is more powerful than the Kruse and KSS tests.     

A Bayesian Hierarchical Model for Multiple Comparisons in Mixed Models

We propose a Bayesian hierarchical model for multiple comparisons in mixed models where the repeated measures on subjects are described with the subject random effects. The model facilitates inferences in parameterizing the successive differences of the population means, and for them, we choose independent prior distributions that are mixtures of a normal distribution and a discrete distribution with its entire mass at zero. For the other parameters, we choose conjugate or vague priors. The performance of the proposed hierarchical model is investigated in the simulated and two real data sets, and the results illustrate that the proposed hierarchical model can effectively conduct a global test and pairwise comparisons using the posterior probability that any two means are equal. A simulation study is performed to analyze the type I error rate, the familywise error rate, and the test power. The Gibbs sampler procedure is used to estimate the parameters and to calculate the posterior probabilities.     

Two non-parametric, analysis-of-means-type tests for homogeneity of variances

After a brief review of the literature, two non-parametric tests for homogeneity of variances are presented. The first test is based on the analysis of means for ranks, which is a non-parametric version of the analysis of means (ANOM) that uses ranks as input for an ANOM test. The second test uses inverse normal scores of the ranks of scale transformations of the observations as input to the ANOM. Both homogeneity of variances tests can be presented in a graphical form, which makes it easy for practitioners to assess the practical and the statistical significance. A Monte Carlo study is used to show that these tests have power comparable with that of well-known robust tests for homogeneity of variances.     

门限自回归下的单位根检验可靠性研究

在非对称的门限自回归模型下,由于传统单位根检验式的误设,会导致单位根检验势下降。本文通过一系列的Monte-Carlo模拟表明：非对称性对ADF和PP检验的检验势会产生较大影响,而对其他四种常用的单位根检验势产生的影响较小,也就是说,在非对称的门限自回归下,非对称性对退势单位根检验势产生的影响较小。模拟中也发现：NP单位根检验对TAR模型和持久性都具有稳健性。     

An empirical goodness-of-fit test for multivariate distributions

An empirical test is presented as a tool for assessing whether a specified multivariate probability model is suitable to describe the underlying distribution of a set of observations. This test is based on the premise that, given any probability distribution, the Mahalanobis distances corresponding to data generated from that distribution will likewise follow a distinct distribution that can be estimated well by means of a large sample. We demonstrate the effectiveness of the test for detecting departures from several multivariate distributions. We then apply the test to a real multivariate data set to confirm that it is consistent with a multivariate beta model.     

Modeling of Discrete HNBUE Class with Hypothesis Testing Application

A new model is proposed to test whether an equipment whose life is measured in discrete time units fails due to uncontrollable chance factors alone against the alternatives that it degrades over time in the sense of discrete HNBUE (harmonic new better than used in expectation) aging. The test is shown to be consistent and the asymptotic distribution of the test statistic has been obtained. The critical points and the power of the test against various alternatives from discrete HNBUE class have been studied by means of simulation. Finally, the test is applied to a discrete reliability data to examine the performance.     

Estimation and hypothesis in linear models-A reparameterization approach to the cell mlans modll

A general approach to analysis of fixed effects models through a reparameterization of the cell means model is outlined. After applying a Q-op3rator, distribution theory for the model is developed. Methods of estimation and hypothesis testing are given and the exact form of each hypothesis is shown. The implementation of these results in a currently available computer package is discussed.     

Exact and approximate distributions for linear contrasts of means and variances

A Bayesian analysis is presented for the K-group Behrens-Fisher problem. Both exact posterior distributions and approximations were developed for both a general linear contrast of the K means and the K variances, given either proper diffuse or informative conjugate priors. The contrast of variances is a unique feature of the heterogeneous variance model that enables investigators to test specific effects of experimental manipulations on variance. Finally, important-differences were observed between the heterogeneous variance model and the homogeneous model.     

Geometric versus arithmetic random walk the case of trended variables

The asymptotic behavior of the empirical means and variances for the geometric and arithmetic random walks are studied, when the underlying random walk is trended. Thus the effect of misspecifications can be described, and two tests are proposed. The first test uses a classical approach in model selection and is based on the comparison of estimated quasi likelihoods. The second one is obtained by estimating some nuisance parameters in a Neyman-Pearson test. Some bounds for the power functions are given, which suggest that the second test may be very powerful and better than the first one.     

On the bivariate negative binomial regression model

In this paper, a new bivariate negative binomial regression (BNBR) model allowing any type of correlation is defined and studied. The marginal means of the bivariate model are functions of the explanatory variables. The parameters of the bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness-of-fit are discussed. Two numerical data sets are used to illustrate the techniques. The BNBR model tends to perform better than the bivariate Poisson regression model, but compares well with the bivariate Poisson log-normal regression model.     

Bayesian generalizations of the integer-valued autoregressive model

We develop two Bayesian generalizations of the Poisson integer-valued autoregressive model. The AdINAR(1) model accounts for overdispersed data by means of an innovation process whose marginal distributions are finite mixtures, while the DP-INAR(1) model is a hierarchical extension involving a Dirichlet process, which is capable of modeling a latent pattern of heterogeneity in the distribution of the innovations rates. The probabilistic forecasting capabilities of both models are put to test in the analysis of crime data in Pittsburgh, with favorable results.     

基于VAR的央行对股票市场影响力分析

文章利用协整和向量自回归工具,通过单位根检验、因果关系检验、协整检验和脉冲分析,从更宽广的视角来分析央行对股票市场的影响力。     

Interpretation of the four types of analysis of variance tables in sas

Various computational methods exist for generating sums of squares in an analysis of variance table. When the ANOVA design is balanced, most of these computational methods will produce equivalent sums of squares for testing the significance of the ANOVA model parameters. However, when the design is unbalanced, as is frequently the case in practice, these sums of squares depend on the computational method used.- The basic reason for the difference in these sums of squares is that different hypotheses are being tested. The purpose of this paper is to describe these hypotheses in terms of population or cell means. A numerical example is given for the two factor model with interaction. The hypotheses that are tested by the four computational methods of the SAS general linear model procedure are specified.

Although the ultimate choice of hypotheses should be made by the researcher before conducting the experiment, this paper

PENDLETON,VON TRESS,AND BREMER

presents the following guidelines in selecting these hypotheses:

When the design is balanced, all of the SAS procedures will agree.

In unbalanced ANOVA designs when there are no missing cells. SAS Type III should be used. SAS Type III tests an unweighted hypothesis about cell means. SAS Types I and II test hypotheses that are functions of the ceil frequencies. These frequencies are often merely arti¬facts of the experimental process and not reflective of any underlying frequencies in the population.

When there are missing cells, i.e. no observations for some factor level combinations. Type IV should be used with caution. SAS Type IV tests hypotheses which depend     

Estimation of Missing Cells in Randomized Block and Latin Square Designs

Classical missing cell formulas for the randomized block design and Latin square design are derived using the modified cell means model. The role of the assumptions of no interaction for these designs is made clear in the development. Examples are given for the randomized block and Latin square.     

Test for model selection using Cramér–von Mises distance in a fixed design regression setting

In this paper a test for model selection is proposed which extends the usual goodness-of-fit test in several ways. It is assumed that the underlying distribution H depends on a covariate value in a fixed design setting. Secondly, instead of one parametric class we consider two competing classes one of which may contain the underlying distribution. The test allows to select one of two equally treated model classes which fits the underlying distribution better. To define the distance of distributions various measures are available. Here the Cramér-von Mises has been chosen. The null hypothesis that both parametric classes have the same distance to the underlying distribution H can be checked by means of a test statistic, the asymptotic properties of which are shown under a set of suitable conditions. The performance of the test is demonstrated by Monte Carlo simulations. Finally, the procedure is applied to a data set from an endurance test on electric motors.     

An easy way to tell what you are esting in analysis of variance

Least squares regression models are often used to analyze unbalanced fixed effect data sets with u unique cells defined by design or by post-hoc stratification. Constraints exist among the regression coefficients if there are more coefficients than cells. Models with fewer linearly independent regression coefficients than cells or with empty cells impose constraints on estimated cell means. An easy method of determining constraints among the estimated cell means and among the estimated regression coefficients for any model is developed and illustrated using a small data set.     

Modelling asymmetric volatility dynamics by multivariate BL-GARCH models

The class of Multivariate BiLinear GARCH (MBL-GARCH) models is proposed and its statistical properties are investigated. The model can be regarded as a generalization to a multivariate setting of the univariate BL-GARCH model proposed by Storti and Vitale (Stat Methods Appl 12:19–40, 2003a; Comput Stat 18:387–400, 2003b). It is shown how MBL-GARCH models allow to account for asymmetric effects in both conditional variances and correlations. An EM algorithm for the maximum likelihood estimation of the model parameters is derived. Furthermore, in order to test for the appropriateness of the conditional variance and covariance specifications, a set of robust conditional moments test statistics are defined. Finally, the effectiveness of MBL-GARCH models in a risk management setting is assessed by means of an application to the estimation of the optimal hedge ratio in futures hedging.