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Two-dimensional distributions whose marginal distributions are uniform are called bivariate copulas. Among them, the one that satisfies given constraints on expectation and is closest to being an independent distribution in the sense of Kullback–Leibler divergence is called the minimum information bivariate copula. The density function of the minimum information copula contains a set of functions called the normalizing functions, which are often difficult to compute. Although a number of proper scoring rules for probability distributions having normalizing constants such as exponential families have been proposed, these scores are not applicable to the minimum information copulas due to the normalizing functions. In this paper, we propose the conditional Kullback–Leibler score, which avoids computation of the normalizing functions. The main idea of its construction is to use pairs of observations. We show that the proposed score is strictly proper in the space of copula density functions and therefore the estimator derived from it has asymptotic consistency. Furthermore, the score is convex with respect to the parameters and can be easily optimized by the gradient methods. [ABSTRACT FROM AUTHOR]

Abstract: We study properties of Fisher distribution (von Mises–Fisher distribution, matrix Langevin distribution) on the rotation group . In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011) [16], and a method of series expansion for evaluating the normalizing constant of the distribution and for computing the maximum likelihood estimate. The rotation group can be identified with the Stiefel manifold of two orthonormal vectors. Therefore from the viewpoint of statistical modeling, it is of interest to compare Fisher distributions on these manifolds. We illustrate the difference with an example of near-earth objects data. [Copyright &y& Elsevier]

Abstract: For the statistical analysis of multiway contingency tables, we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving the localization property of the inference in the hierarchical model. This approach also enables us to evaluate the localization property of a given log-affine model. We discuss estimation and exact tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets. [Copyright &y& Elsevier]

We propose a new parametric model for continuous data, a 'g-model', on the basis of gradient maps of convex functions. It is known that any multivariate probability density on the Euclidean space is uniquely transformed to any other density by using the gradient map of a convex function. Therefore the statistical modeling for quantitative data is equivalent to design of the gradient maps. The explicit expression for the gradient map enables us the exact sampling from the corresponding probability distribution. We define the g-model as a convex subset of the space of all gradient maps. It is shown that the g-model has many desirable properties such as the concavity of the log-likelihood function. An application to detect the three-dimensional interaction of data is investigated. [ABSTRACT FROM AUTHOR]

Abstract: An information criterion for models with local asymptotic mixed normality (LAMN) is proposed. Since the widely known Akaike's Information Criterion (AIC) is derived on the basis of local asymptotic normality (LAN), it cannot be directly used to model selection of LAMN models, and so a criterion for these models is required. The proposed criterion for LAMN models is an asymptotically unbiased estimator of the Kullback–Leibler risk of Bayesian prediction. We present the results of simulation studies for a mixed normal model, a discretely observed diffusion model and a partially explosive Gaussian AR model. [Copyright &y& Elsevier]