On testing hypotheses in two-sample problems, the Lepage-type statistic is often used for testing the location and scale parameters. Various Lepage-type statistics have been proposed and discussed by many authors over the course of many years. One of the most famous and powerful Lepage-type statistics is a combination of the Wilcoxon and Mood statistics, namely T. Deriving the exact critical value of the T statistic is difficult when the sample sizes are increased. In that situation, an approximation to the distribution function of a test statistic is extremely important in statistics. The gamma approximation and the saddlepoint approximations are used to evaluate in upper tail probability for the T statistic under finite sample sizes. The accuracy of various approximations to the exact probability of the T statistic is investigated.

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We consider power-transformations to obtain stability and invariance of measurement scale. The transformation discussed here is the normalized form of the power-transformation originally suggested by Schlesselman (1971). The original suggestion is a simple modification of the Box and Cox transformation to scale invariance for measurement units. In addition to discussion on the scale invariance, we study (i) the behaviors of Jacobian of the transformation and (ii) the effect of the modification on the estimates. Then, we show that the modification of the scale invariance improves the performance of estimates, especially the mean estimate. A simulation study is performed to evaluate numerically performances of the modified transformation, compared with the normalized Box and Cox transformation.

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ABSTRACT For square contingency tables with ordered categories, Agresti (2002) considered the ordinal quasi-symmetry (OQS) model and Iki, Tahata and Tomizawa (2009) considered the ridit score type quasi-symmetry (RQS) model. The present paper proposes measures which represent the degree of departure from each of the OQS and RQS mod els. The proposed measures are expressed by using the Cressie-Read power-divergence or Patil-Taillie diversity index. These measures would be useful for comparing the de grees of departure from OQS and RQS in several tables. The measures are applied to the data of individual's education and father's or mother's education in Japan.

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In this article, we derive the observed information matrices for normal mixture models and normal hidden Markov models. We also describe the parametric bootstrap method for the said models. The matrices and the method mentioned above are used to estimate the variance of the maximum likelihood estimates (MLEs) obtained by the Expectation-Maximization (EM) algorithm. Finally, a numerical example is shown using a data set named " faithful " given in the free statistical software R.

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ABSTRACT In recent years, attention has been focused on estimating average treatment effects in statistics, economics, epidemiology and so on. For example, effects of job training in economics, or comparing treatment effects in epidemiological studies are frequently studied. There is a lot of literature on estimating the average treatment effect of a binary treatment variable under some assumptions. Some of them use parametric methods, and some use semiparametric methods. This paper firstly describes the role of Rubin’s causal model, reviews various methods for estimating the average treatment effects, then proposes one combined method (subclassification matching method) to estimate the average treatment effect. Extensive simulations are carried to compare all the methods. We find that the proposed mixed methods are better than other methods considered here.

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