In this study we discuss multiple comparison procedures for checking differences among a sequence of normal means with ordered restriction. Lee and Spurrier (1995) proposed a single step multiple comparison procedure checking difference between adjacent two means. There exists two kinds of stepwise multiple comparison procedures developing Lee and Spurrier (1995). Shiraishi (2014) proposed a step down multiple comparison procedure based on closed testing procedure. Douke et al. (2006) proposed a sequentially rejective multiple comparison procedure. In this study we propose a step up multiple comparison procedure developing Lee and Spurrier (1995). We give numerical results regarding critical values for a specified significance level and power of the test intended to compare single step procedure and three kinds of stepwise procedures.

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We consider multiple comparisons tests for the differences among mean responses in k normal populations．Hayter (1990) proposed single-step procedure as all-pairwise comparison test between ordered treatments. Lee and Spurrier (1995) also discussed single-step procedure as successive comparison test. Shiraishi (2014) proposed closed testing procedures which are superior to Hayter (1990) and Lee and Spurrier (1995). To execute the closed testing procedures, Shiraishi (2014) utilized the upper 100α^★th percentiles of the distribution of max_i<i′ (−t_ii′), where α^★=1−(1−α)^ℓ/M (2 ≦ ℓ ≦ M ≦ k) and t_ii''s denote the two sample t test statistics. We investigate the properties of the density functions which appear in the distribution of max_i<i′ (−t_ii′). Based on it, we show these density functions are approximated efficiently with using sinc method described in Lund and Bowers (1992) and Stenger (1993). Finally, we describe the algorithm to calculate upper 100α^★%th percentiles of the closed testing procedure superior to Hayter (1990). Numerical examples are given to demonstrate the performance of our scheme.

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In this study, we propose a multiple comparison procedure for detecting sequentially a lowest dose having interaction based on the obtained observations by the sequential dose response experiment of cell-wise in the two-way table. For realizing our procedure, we apply group sequential procedure to our procedure that tests sequentially the null hypotheses of no interaction based on tetrad differences. If we can first detect a dose having interaction at an early stage in the sequential test, it is possible to terminate the procedure with a few observations up to the stage. Thus, the procedure is useful from an economical point of view when high costs are involved for obtaining the observations. In the procedure, we induce an integral formula to determine the repeated confidence boundaries for satisfying a predefined type I familywise error rate. Furthermore, we show how to decide the required sample size at each cell with guaranteeing the power of the test in the procedure. In the simulation studies, we compare the superiority among the procedures based on three α spending functions in terms of the power of the test and the required sample size for various configurations of population means.

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In this paper, we discuss multivariate multiple comparison among mean vectors in high-dimensional settings. In particular, in the case of pairwise comparisons, we propose procedures that construct the approximate simultaneous confidence intervals. We review the results of asymptotic expansions for the upper 100α percentiles of our proposed statistic. Also, we derive the asymptotic null distribution for this statistic under non-normality. Finally, numerical results by Monte Carlo simulations are given.

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In the standard formulation of factor analysis (FA), factor loadings and unique variances are treated as fixed parameters, while common and unique factors are regarded as latent random variables. A very different formulation of FA has recently been presented in which common and unique factors are also treated as parameters and all model parts are expressed as parameter matrices. This is referred to as matrix factor analysis (MFA), whose properties are discussed in this paper. It is shown that the MFA algorithm is clearly described with concepts in linear algebra and allows FA to be viewed as higher rank approximation of a data matrix in contrast to principal component analysis as lower rank approximation. We further give numerical illustrations for comparing MFA solutions with the standard FA ones and discuss a sparse FA procedure derived from MFA.

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In this paper, I will give a brief introduction to a data analysis technique called non-negative matrix factorization (NMF), which has attracted a lot of attention in the field of audio signal processing in recent years. I will mention some basic properties of NMF, effects induced by the non-negative constraints, how to derive an iterative algorithm for NMF, and some attempts that have been made to apply NMF to audio processing problems.

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Tensors are multiarray data of real (complex) cell values similar to contingency tables of integer cell values which is familar to statisticians. Needless to say, multiway data arise in various applied field and theorefore the need of methods of analysing such array data is quite high. The essence of data analysis is in decomposing data and extracting important components. In this article, we focus on the parafac decomposition of multiarray datum and especially on rank problem of PARAFAC decompositions from computational algebraic views.

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In dynamic discrete choice analysis in econometrics, controlling for unobserved heterogeneity is an important issue. Finite mixture models provide flexible ways to account for it, and have been used in numerous applications. However, until recently, pessimistic views were prevalent on the nonparametric identifiability of finite mixture models of dynamic discrete choices, because little was known of nonparametric identifiability of mixture models. We review Kasahara and Shimotsu (2009, 2014a), and introduce sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under different assumptions on the time-dimension of panel data, stationarity, and Markov property. We also discuss nonparametric identifiability of the lower bound for the number of components in finite mixture models and provide an estimation procedure for the number of components.

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Concerning a stochastic differential equation driven by a non-Gaussian Lévy process, we outline construction and asymptotic behavior of the Gaussian quasi-maximum-likelihood estimator and self-normalized-residual based test statistics for noise-normality and diffusion-coefficient misspecification.

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