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Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured densities to “star-shaped distributions” with concentric starshaped contours and show that many results in the former case continue to hold in the more general case.… (More)

In the unidimensional unfolding model, given m objects in general position on the real line, there arise 1 + m(m − 1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. Change of the position of these m objects results in change of the ranking pattern. In this paper we use arrangement theory to determine the number of… (More)

Consider the problem of pairwise linear discriminant analysis among m populations in R: For each pair of populations, we have a discriminant hyperplane. Then R is divided into regions by m(m 1)=2 such hyperplanes. Each region is indexed by an ordering of m populations, with the nearest population assigned the rank 1; the second nearest the rank 2; and so… (More)

This paper is concerned with a study of robust estimation in principal component analysis. A class of robust estimators which are characterized as eigenvectors of weighted sample covariance matrices is proposed, where the weight functions recursively depend on the eigenvectors themselves. Also, a feasible algorithm based on iterative reweighting of the… (More)

Let q be a positive integer. In [8], we proved that the cardinality of the complement of an integral arrangement, after the modulo q reduction, is a quasi-polynomial of q, which we call the characteristic quasi-polynomial. In this paper, we study general properties of the characteristic quasi-polynomial as well as discuss two important examples: the… (More)

We study central hyperplane arrangements with integral coefficients modulo positive integers q. We prove that the cardinality of the complement of the hyperplanes is a quasi-polynomial in two ways, first via the theory of elementary divisors and then via the theory of the Ehrhart quasi-polynomials. This result is useful for determining the characteristic… (More)

Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model.

We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all braid slices, including those not associated with unfolding models, are in one-to-one correspondence with the chambers of… (More)

We study properties of global cross sections and characterize the class of all global cross sections. Then generalizing the cross-sectionally contoured distributions of Takemura and Kuriki (1996), we de ne the decomposable distributions with respect to a global cross section. The distributional results about the invariant and equivariant parts remain to… (More)

- Shozo Fukuda, Hidehiko Kamiya
- Conference Record of the 2001 IEEE Industry…
- 2001

An active filter (AF) is required to have a high current control capability of tracking a time-varying current reference. However, a steady-state current error always exists because the current reference varies in time. This paper proposes the application of adaptive digital signal processing (ADSP) to the current control of AF. ADSP does not require any… (More)