In this paper, we consider profile analysis of several groups where the groups have partly equal means. This leads to a profile analysis for a growth curve model. The likelihood ratio statistics are given for the three hypotheses known in literature as parallelism, level hypothesis and flatness. Furthermore, exact and asymptotic distributions are given in the relevant cases.

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A class of curved exponential families whose likelihood function admits the conjugate analysis is derived, and its duality is explored. We show that conjugacy yields the existence of sufficient statistics as well as duality. Extended versions of the mean and the canonical parameters can be defined, which shed a new light on duality and the conjugate analysis in the exponential family. As a result, an essential reason is revealed as to why a common prior density can be conjugate for different sampling densities, as in the case of a gamma prior density which is conjugate for the Poisson and the gamma sampling densities. The least information property of the conjugate analysis is explained, which is compatible with the minimax property of the generalized linear model. We also derive dual Pythagorean relationships with respect to posterior risks to show the optimality of the Bayes estimator.

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In this paper, a modified inverse stereographic projection, from the real line to the circle, is used as the motivation for a means of resolving a discontinuity in the Minh–Farnum family of circular distributions. A four-parameter family of symmetric unimodal distributions which extends both the Minh–Farnum and Jones–Pewsey families is proposed. The normalizing constant of the density can be expressed in terms of Appell's function or, equivalently, the Gauss hypergeometric function. Important special cases of the family are identified, expressions for its trigonometric moments are obtained, and methods for simulating random variates from it are described. Parameter estimation based on method of moments and maximum likelihood techniques is discussed, and the latter approach is used to fit the family of distributions to an illustrative data set. A further extension to a family of rotationally symmetric distributions on the sphere is briefly made.

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We study the impact of individual and temporal aggregation in linear static and dynamic models for panel data in terms of i) model specification, ii) efficiency of the estimated parameters, and iii) the choice of the aggregation scheme. Model wise we find that i) individual aggregation does not affect the model structure but temporal aggregation may introduce residual autocorrelation, and ii) individual aggregation entails heteroscedasticity while temporal aggregation does not. Estimation and aggregation scheme wise we find that i) in the static model, estimation by least squares with the aggregated data entails a decrease in the efficiency of the estimated parameters and no aggregation scheme dominates in terms of efficiency, and ii) in the dynamic model, estimation with the aggregated data by GMM does not necessarily entail a decrease in the efficiency of the estimated parameters under individual aggregation, and no analytic comparison can be established for temporal aggregation, though simulations suggests that temporal aggregation deteriorates the accuracy of the estimates.

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For multi-way tables with ordered categories, Tahata et al.\ (2008) considered the collapsed symmetry model, which indicates the symmetry for the tables collapsed the original table by choosing the cut point in the categories. The present paper proposes a measure to represent the degree of departure from collapsed symmetry for multi-way tables. The measure proposed is expressed by using the Cressie-Read power-divergence or the Patil-Taillie diversity index. The measure would be useful for comparing the degrees of departure from collapsed symmetry in several multi-way tables. Examples are given.

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The paper addresses the problem of selecting variables in linear mixed models (LMM)νll. We propose the Empirical Bayes Information Criterion (EBIC) using a partial prior information on the parameters of interest. Specifically EBIC incorporates a non-subjective prior distribution on regression coefficients with an unknown hyper-parameter, but it is free from the setup of a prior information on the nuisance parameters like variance components. It is shown that EBIC not only has the nice asymptotic property of consistency as a variable selection, but also performs better in small and large sample sizes than the conventional methods like AIC, conditional AIC and BIC in light of selecting true variables.

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Let \{Y_n\} be a sequence of nonnegative random variables (rvs), and S_n=∑_j=1ⁿY_j, n≥1. It is first shown that independence of S_k-1 and Y_k, for all 2≤ k≤n, does not imply the independence of Y₁,Y₂,...,Y_n. When Y_j's are identically distributed exponential \Exp(α) variables, we show that the independence of S_k-1 and Y_k, 2W≤k≤n, implies that the S_k follows a gamma G(α,k) distribution for every 1≤k≤n. It is shown by a counterexample that the converse is not true. We show that if X is a non-negative integer valued rv, then there exists, under certain conditions, a rv Y≥ 0 such that N(Y)\stackrel{\cal{L}}{=}X, where {N(t)} is a standard (homogeneous) Poisson process, and obtain the Laplace-Stieltjes transform of Y. This leads to a new characterization for the gamma distribution. It is also shown that a G(α,k) distribution may arise as the distribution of S_k, where the components are not necessarily exponential. Several typical examples are discussed.

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We model large panels of financial time series by means of generalized dynamic factor models with multivariate GARCH idiosyncratic components. Such models combine the features of dynamic factors with those of a generalized smooth transition conditional correlation (GSTCC) model, which belongs to the class of time-varying conditional correlation models. The model is applied to dynamic portfolio allocation with Value at Risk constraints on 6.5 years of daily TOPIX Sector Indexes. Results show that the proposed model yields better portfolio performance than other multivariate models proposed in the literature, including the traditional mean-variance approach.

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The portfolio of the Japanese Government Pension Investment Fund (GPIF) consists of a linear combination of five benchmarks of financial assets. Some of these exhibit long-memory and nonlinear behavior. Their analysis therefore requires multivariate nonlinear and long-memory time series models. Moreover, the assumption that the innovation densities underlying those models are known seems quite unrealistic. If those densities remain unspecified, the model becomes a semiparametric one, and rank-based inference methods naturally come into the picture. Rank-based inference methods under very general conditions are known to achieve the semiparametric efficiency bounds. % through the maximum invariant property of ranks. Defining ranks in the context of multivariate time series models, however, is not obvious. We propose two distinct definitions. The first one relies on the assumption that the innovation density is some unspecified elliptical density. The second one relies on the assumption that the innovation process is described by some unspecified independent component analysis model. Applications to portfolio management problems are discussed.

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