This article describes a semiparametric estimation method for a discrete duration model with autoregressive random effects using Markov chain Monte Carlo techniques, and analyzes the duration of ten monthly economic times series which are components of the Japanese leading diffusion index. By introducing common time-dependent random effects to the individual duration, we capture a co-movement among durations that represents external macroeconomic factors. A dynamic modelling approach is employed assuming smoothness conditions on the baseline hazard function for long duration times with sparse observations.

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The threshold method in the framework of marked spatial point processes on a continuous space is discussed. The threshold method is a linear prediction of the total sum of marks using only the number of points with marks exceeding a given threshold value. The result is an extension of Mase (1996) to a continuous space and also the independent mark assumption of Mase (1996) is weakened. It is shown that the total sum of the marks is linearly predictable if the number of points has a huge variation and marks satisfy some mixing condition. A simulation study is given to illustrate the theoretical result.

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Stein-type estimation of location vectors is discussed with the aid of the theory of electrostatics. We consider a class of estimating functions and assess the superiority of an estimating equation by its mean squared norm. The Coulomb potential function leads to a Pythagorean relationship with respect to this norm. By making full use of the Pythagorean relationship, we improve upon the likelihood estimating function. A further improvement is shown to be feasible under a certain condition which is described. We pursue possible strong relationships between the superiority over the likelihood estimating function and physical quantities appearing in the theory of electrostatics.

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In the present paper, we consider the problem of estimating a ratio ρ = E(Y) / E(X) in a regression model Y = α + βX + U. We obtain the higher order approximation of the probability distribution of the usual ratio estimator based on the sample means. In the gamma, lognormal and exponential cases, the approximation is numerically compared with the normal one and the empirical distribution. We also consider the higher order approximation of the percentage point and the construction of the confidence interval by using the approximation.

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As an estimator of an estimable parameter, Toda and Yamato (2001) introduced a linear combination Y_n of U-statistics which includes V-statistic and LB-statistic. We give the Edgeworth expansions of the standardized Y_n statistic with remainder o(n^-1) in case that the kernel is not degenerate. We also give the Edgeworth expansions of the studentized Y_n statistic using a jackknife variance estimator with remainder o(n^-1/2).

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This paper characterizes the distributions of power inverse Gaussian and others based on the entropy maximization principle (E.M.P.) and discuss the relationships of these distributions to the log-normal and the inverse Gaussian distributions. Moreover, the power Birnbaum-Saunders and the generalized Gumbel distribution are characterized under some constraints.

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The present article describes a Conditional Inverse Gaussian-Poisson (CIGP) distribution, obtained by conditioning an inverse Gaussian-Poisson population model on its total frequency. This CIGP distribution is equivalent to random partitioning of positive integers, with the possibility for a number of applications in statistical ecology, linguistics and statistical disclosure control to name a few. After showing the marginal moments of the distribution, parameter estimation is discussed. Fitting the CIGP distribution to some typical data sets demonstrates its applicability.

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The preliminary test ridge regression estimators (PTRRE) based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are considered in this paper. Using risks, the regions of optimality of the estimators are determined. Under the null hypothesis, the PTRRE based on LM test has the smallest risk followed by the estimators based on LR and W tests. However, the PTRRE based on W test performs the best followed by the LR and LM based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimator for both shrinkage parameter and departure parameter are given. Some tables for maximum and minimum guaranteed relative efficiency of the proposed estimators have been provided. These tables allow us to determine the optimum level of significance corresponding to the optimum estimators among proposed estimators. Finally, we conclude that the optimum choice of the level of significance becomes the traditional choice by using the W test for all non-negative shrinkage parameter.

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This paper describes some new patterned methods of constructing rectangular designs from balanced incomplete block (BIB) designs and nested BIB designs, and gives a table of rectangular designs in the range of r, k ≤ 10.

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