A circular-cone test for testing homogeneity against a simple tree order

Several methods exist for the problem of testing the equality of several treatments against the one-sided alternative that the treatments are better than the control. These methods include Dunnett's test, Bartholomew's likelihood-ratio test, the Abelson-Tukey-Schaafsma-Smid optimal-contrast test, and the multiple-contrast test of Mukerjee, Robertson, and Wright. A new test is proposed based on an approximation of the likelihood-ratio test of Bartholomew. This test involves using a circular cone in place of the alternative-hypothesis cone. The circular-cone test has excellent power characteristics similar to those of Bartholomew's test. Moreover, it has the advantages of being simpler to compute and may be used with unequal sample sizes.     

简论语料库与教师角色之转变

现代电子语料库已有了近50年的发展,但语料库应用于课堂教学才刚刚起步。通过近年语料库辅助课堂教学诸多实践研究,教师们不仅可以获得教学中的例句,还可引导学生们学习更地道、更准确的表达方式。     

New imperfect rankings models for ranked set sampling

Ranked set sampling is a sampling approach that leads to improved statistical inference in situations where the units to be sampled can be ranked relative to each other prior to formal measurement. This ranking may be done either by subjective judgment or according to an auxiliary variable, and it need not be completely accurate. In fact, results in the literature have shown that no matter how poor the quality of the ranking, procedures based on ranked set sampling tend to be at least as efficient as procedures based on simple random sampling. However, efforts to quantify the gains in efficiency for ranked set sampling procedures have been hampered by a shortage of available models for imperfect rankings. In this paper, we introduce a new class of models for imperfect rankings, and we provide a rigorous proof that essentially any reasonable model for imperfect rankings is a limit of models in this class. We then describe a specific, easily applied method for selecting an appropriate imperfect rankings model from the class.     

Wavelet goodness-of-fit test for dependent data

We introduce a new goodness-of-fit test which can be applied to hypothesis testing about the marginal distribution of dependent data. We derive a new test for the equivalent hypothesis in the space of wavelet coefficients. Such properties of the wavelet transform as orthogonality, localisation and sparsity make the hypothesis testing in wavelet domain easier than in the domain of distribution functions. We propose to test the null hypothesis separately at each wavelet decomposition level to overcome the problem of bi-dimensionality of wavelet indices and to be able to find the frequency where the empirical distribution function differs from the null in case the null hypothesis is rejected. We suggest a test statistic and state its asymptotic distribution under the null and under some of the alternative hypotheses.     

A Question of Ethics

This article identifies three consulting roles—helper, leader, and colleague; recommends that statistical consultants ask more questions about basic mechanisms; suggests that statistical consultants regard their primary responsibility as providing guidance about the scientific method itself; discusses the need for continuing education to help improve consulting skills; and describes Wisconsin's Master's degree examination, which was designed to help students become effective practicing statisticians.     

Non-Normal Bivariate Distributions with Normal Marginals

The purpose of this note is to indicate that Fieller's Theorem can be expressed in the matrix formulation of the general linear model. The practical consequence is that one general computer program which can estimate the parameters and test the validity of a pertinent model, can also compute confidence limits for the ratios of any linear combinations of the parameters.     

Pmc-optimal nonparametric quantile estimator

According to Pitman's Measure of Closeness, if T₁and T₂are two estimators of a real parameter $[d], then T₁is better than T₂if Po[d]{T₁-o[d] < T₂-0[d]} > 1/2 for all 0[d]. It may however happen that while T₁is better than T₂and T₂is better than T₃, T₃is better than T₁. Given q ? (0,1) and a sample X₁, X₂, ..., X_nfrom an unknown F ? F, an estimator T* = T*(X₁,X₂...X_n)of the q-th quantile of the distribution F is constructed such that P_F{F(T*)-q <[d] F(T)-q} >[d] 1/2 for all F?F and for all T€T, where F is a nonparametric family of distributions and T is a class of estimators. It is shown that T* =X_j:n'for a suitably chosen jth order statistic.     

Data-dependent probability matching priors of the second order

In this paper, we consider the preliminary test approach for the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The preliminary test two-parameter estimators based on the Wald (W), likelihood ratio, and Lagrangian multiplier tests are given, when it is suspected that the regression parameter may be restricted to a subspace and the regression error is distributed with multivariate Student's t distribution. The bias and mean square error of the proposed estimators are derived and compared. The conditions of superiority of the proposed estimators are obtained. Finally, we conclude that the optimum choice of the level of significance becomes the traditional choice by using the Wald test.     

Testing Equality of Mean Vectors in Two Sample Problem with Missing Data

Finding the influence of traffic accident on the road is helpful to analyze the characteristics of traffic flow, and take reasonable and effective control measures. Here, the detrended fluctuation analysis method is applied to investigate the complexity of time series in mixed traffic flow with a blockage induced by an accident. As a parameter to depict the long-term evolutionary behavior of the time series in traffic flow, the scaling exponent is analyzed. According to the scaling exponent, it is shown that the traffic flow time series can display long-range correlation characteristics, short-range correlation characteristics, and non-power-law relation in the long-range correlation characteristics, which is strongly dependent on the entering probability of vehicle, the ratio of slow vehicle and the blockage duration time.