Asymmetrical movements between the downward and upward phases of sample paths of many financial time series have been noted by economists. By incorporating the conditional heteroskedasticity aspect into the nonstationary simultaneous switching autoregressive (SSAR) model, the asymmetrical volatility function of financial time series with daily effects can be easily estimated. We report a simple empirical result for stock price daily indices of the Nikkei-225 and SP-500 using this model.

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This paper considers the count model with endogenous switching proposed by Terza (1998) from a Bayesian point of view. We consider Markov chain Monte Carlo methods to estimate the parameters of the model. Furthermore, an extension is made to handle the case of non-normality and model determination is discussed. Our approach is illustrated with both simulated and real data sets.

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We obtained estimation results concerning a progressively type-II censored sample from a two-parameter Weibull distribution. The maximum likelihood method is used to derive the point estimators of the parameters. An exact confidence interval and an exact joint confidence region for the parameters are constructed. A numerical example is presented to illustrate the methods proposed here.

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The problem of estimation in multivariate linear calibration with multivariate response and explanatory variables is considered. In this calibration problem two estimators are well-known; one is the classical estimator and the other is the inverse estimator. In this paper we show that the inverse estimator is a proper Bayes estimator under the quadratic loss with respect to a prior distribution which is considered by Kiefer and Schwartz (1965, Ann. Math. Statist., 36, 747-770) for proving admissibility of the likelihood ratio test about equality of covariance matrices undre the normality assumption. We also show that the Bayes risk of the inverse estimator is finite and hence the inverse estimator is admissible under the quadratic loss. Further we consider an improvement on the classical estimator under the quadratic loss. First, the expressions for the first and the second moments of the classical estimator are given with expectation of a function of a noncentral Wishart matrix. From these expressions, we propose an alternative estimator which can be regarded as an extension of an improved estimator derived by Srivastava (1995, Commun. Statist.-Theory Meth., 24, 2753-2767) and we show, through numerical study, that the alternative estimator performs well as compared with the classical estimator.

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We consider tests of dimensionality in the multivariate analysis of variance (MANOVA). Three types of test criteria (Likelihood-Ratio-type, Lawley-Hotelling-type and Bartlett-Nanda-Pillai-type) are popular. As is well known, their null distributions depend on nuisance parameters. When a sample size is large, these criteria are distributed approximately according to chi-squared distributions. However, when the sample size is small, the effect of the nuisance parameters cannot be ignored. Under normal populations, other criteria that do not depend on nuisance parameters were proposed. These criteria are also upper limits for the null distributions of LR-type and LH-type. Under elliptical populations, modified test criteria with a better chi-squared approximation were proposed in the case of a large sample. In this paper, we generalize Schott’s results under elliptical populations and obtain new test criteria that do not depend on nuisance parameters.

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We consider an orthogonally invariant estimation of Σ of Wishart distribution using Stein’s loss (entropy loss) or a quadratic loss. In these problems the best lower triangular matrix invariant estimators are minimax estimators. Some orthogonally invariant estimators were derived from those minimax estimators. It is conjectured that they are also minimax estimators, but some estimators have not yet been proved to be minimax. In this paper we prove the minimaxity of some estimators when the dimension is two. We also present the necessary conditions for a class of estimators to be minimax when the dimension is two.

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This paper shows the validity of the (arbitrary) higher order Edgeworth expansion for the distribution of estimators of the coefficient parameter θ∈(−1, 1) in the AR(1) process {X_t} with a possibly nonzero initial value X₀=x. The stationary case of X₀∼N(0, 1/(1−θ²)) is also treated.

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This paper aims at balancing between characterization and modeling approaches for bivariate extensions of univariate life distributions using reversed hazard rates. The proposed model, a characterized one, admits important properties irrespective of the choice of the univariate marginals. The retention of a univariate class property has been ensured along with a result on parallel combination of a bivariate system.

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