ABSTRACT When the research outcome is counts of a rare event, Poisson distribution is a rst choice to describe the population distribution under study. However in some applications, the zero count would not be observed at all. In such cases the model to be tted to the data is a zero-truncated Poisson (ZTP) distribution. This distribution is a special case of the more general zero-modied Poisson (ZMP) distribution family. This article discusses estimation procedures for the Poisson parameter of the ZTP model.In particular, performance of condence intervals in terms of coverage probability is fully examined by Monte Carlo simulations. It is shown that the score-type interval behaves well but the Wald-type interval gives unsatisfactory results if the Poisson mean is small and/or sample size is not so large. A modication of the Wald-type interval is also given, and its performance is investigated by using simulations. The ndings are also applicable to ZMP distributions.

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ABSTRACT In this paper, we investigated the detection of geometric anisotropy (GA) using four directional variograms that produce four sets of parameters. Four angles and corresponding ranges, which are the parameters of the directional variogram models,were used for tting ellipse parameters to detect GA. The tted ellipse indicates the GA determined by the ratio between the semi-major and the semi-minor axes and the rotated angles of the semi-major axis. Another way of detecting GA is to use the likelihood of the data prediction process (the maximum likelihood method). We performed simulation experiments to compare these two methods for detecting GA in addition to a third method that assumes isotropy. Such simulation experiments generate various kinds of GA to evaluate the validity of the three methods. The results of the simulation study showed that, in the case of a small number of data or strong GA,our method provided good results. In contrast, the other two methods only occasionally produced good results.

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ABSTRACT A data-fitting factor analysis (FA) procedure was recently presented, which is very different from the prevailing covariance-fitting FA. In the former procedure, common and unique factor scores are modeled as fixed unknown parameters, and an unweighted least squares (ULS) function, which is not scale invariant, is minimized for fitting the model to a data matrix. The main purpose of this paper is to settle four remaining problems with data-fitting FA. First, we present a weighted least squares (WLS) procedure which can be scale invariant, and include the above ULS procedure as a special case according to the choice of weights. Second, we prove that the WLS loss function can be minimized, even if raw data are unknown and only their sample covariance matrix is available, despite being a data-fitting approach. Third, we propose an estimator of factor scores that cannot be uniquely determined. Fourth, we empirically compare this data-fitting FA procedure with covariance-fitting FA with respect to recovery of parameter matrices.

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ABSTRACT In this paper, we focus on the univariate two-sample Baumgartner statistic and propose a modification of the B statistic for the shifted-scale parameter. A nonparametric rank test based on the Baumgartner statistic was used to test location, scale, and location-scale parameters. Critical values of the test statistics were evaluated; limiting distributions were derived under the null hypothesis. We investigated the power of the proposed statistics by simulation studies. The results of our simulations indicated that the B2 statistic was superior to the B1 statistic for the shifted scale parameters when the sample sizes were equal under symmetric distributions. The differences between these two statistics were small when the sample sizes were unequal. The B2 statistic is more efficient than other nonparametric statistics.

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ABSTRACT When all components of a normal mean vector are simultaneously nonnegative or nonpositive, we consider a multivariate test for checking whether at least one component is nonzero based on the likelihood ratio test. First, we assume that the covariance matrix is known. Next, we assume that it is unknown. In both cases, we consider the determination of the critical value for a specified significance level. Since it is difficult to determine the distributions of the likelihood ratio test statistics, we obtain an approximate critical value using two methods, namely computation using grids and Monte Carlo integration. We give numerical examples regarding critical values intended to compare these methods.

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