Fisher's logarithmic series model (Fisher et al. (1943)) is a classical model in statistical ecology. In this paper we show that this model is a key model linking three models discussed in Takemura (1997), i.e., Poisson-gamma model (Bethlehem et al. (1990)), Dirichlet-multinomial model (Takemura...

We consider the same problem as in Kamiya and Takemura(1997), but for discriminant analysis on (n-1)-dimensional unit sphere s n-1. That is, we regard pairwise discriminant analysis of m populations on s n-1 as a process to generate rankings among the populations, and give a formula for the...

In Kuriki and Takemura (1997a) we established a general theory of James-Stein type shrinkage to convex sets with smooth boundary. In this paper we show that our results can be generalized to the case where shrinkage is toward smooth non-convex cones. A primary example of this shrinkage is...

Let Z be a k-way array whose q1 x...x qk elements are independent standard normal variables. For qi-dimensional vector hi, i=1, ...., k, define a multilinear form of degree k by (h1 x hk)'vec(Z). We derive formulas for upper tail probabilities of the maximum of multilinear form with respect to...

McKay, Conover and Beckman (1979) introduced Latin hypercube sampling (LHS) for reducing variance of Monte Carlo simulations. More recently Owen (1992a) and Tang (1993) generalized LHS using orthogonal arrays. In the Owen's class of generalized LHS, we define extended Latin hypercube sampling of...

In Takemura and Kuriki(1999b) we have established that the tube formula and the Euler characteristic method give identical and valid asymptotic expansion of tail probability of the maximum of Gaussian random field when the random field has finite Karhunen-Loeve expansion and the index set has...

The number of the unique individuals in the population is of great importance in evaluating the disclosure risk of a microdata set. We approach this problem by considering some basic superpopulation models including the gamma-Poisson model of Bethlehem et al.(1990). We introduce...

We give James-Stein type estimators of multivariate normal mean vector by shrinkage to closed convex set K with smooth or piecewise smooth boundary. The rate of shrinkage is determined by the curvature of boundary of K at the projection point onto K. By considering a sequence of polytopes Kj...

Consider a Gaussian random field Z(u) with mean 0, variance 1, and finite Karhunen-Loeve expansion. Under a very general assumption that the index set M is a manifold with piecewise smooth boundary, we prove the validity and the equivalence of two currently available methods for obtaining the...

In the framework of disclosure control of a microdata set, an unique record is at risk of being identified. Even if a record is not unique in the microdata set, it may be considered risky if the frequency k of the cell, in which the record falls, is small. The notion of minimum unsafe...