S U M M A R Y We describe a parametrization of moment tensors that is suitable for use in algorithms for moment tensor inversion. The parameters are conceptually natural and can be easily visualized. The ingredients of the parametrization are present in the literature; we have consolidated them into a concise statement in a geometric setting. We treat several familiar moment tensor topics in th...

We give a classification of Borel measurable, SL(d) covariant or contravariant, homogeneous, vector valued valuations on the space of ddimensional convex polytopes containing the origin in their interiors. The only examples are moment vectors of polytopes and moment vectors of polar polytopes. MSC 2000: 52B45, 52A38.

We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.

This paper studies estimation of a conditional moment restriction model using the nonparametric maximum likelihood approach proposed by Gallant and Nychka (1987). Under some sufficient conditions, we show that the estimator of some finite dimensional parameters is asymptotically normally distributed and attains the semiparametric efficiency bound and that the estimator of the density function i...

Abstract In this paper we consider the problem of pricing a general Asian basket spread option. We develop approximations formulae based on comonotonicity theory and moment matching methods. We compare their relative performances and explain how to choose the best approximation technique as a function of the Asian basket spread characteristics. We also give the Greeks for our proposed methods. ...

The behavior of vector fields under translation, rotation and scaling differs withrespect to the underlying application. Moment invariants that are customized tothe specific problem can be constructed by means of normalization.In this paper, we calculate general TRS (translation, rotation, and scaling) mo-ment invariants for two-dimensional vector fields. As an example, we s...

where χ(1) denotes the dimension of the character χ and (n)k = n(n − 1) · · · (n − k + 1). Thus [8, (7.6)(ii)][12, p. 349] χ(1) is the number f of standard Young tableaux of shape λ. Identify λ with its diagram {(i, j) : 1 ≤ j ≤ λi}, and regard the points (i, j) ∈ λ as squares (forming the Young diagram of λ). We write diagrams in “English notation,” with the first coordinate increasing from to...

We consider estimation of bounds determined by multiple features of the data, such as bounds arising from two or more moment inequalities. In such problems, conventional estimators of the boundaries are known to be biased, and test statistics do not have standard limit distributions, at least at certain points in the parameter space. We use a limit of experiments framework to give a characteriz...

The problem of nding elliptical shapes in an image on a pyramid architecture using moment properties is considered. Based on the moment principle, the proposed method can be employed to determine the ve parameters of an elliptical shape in a given image, including the coordinates of the center of the ellipse, the length of minor and major axes, and the rotation angle of the major axis. A simula...

Let λ = (λ1, λ2, . . . , λm) be a partition of size n, i.e., the λi are weakly decreasing positive integers summing to n. We can represent λ by means of its Young (or Ferrers) diagram, which consists of a collection of left-justified rows where row i contains λi cells. To each of these cells B one associates its hook length, that is, the number of cells in the Young diagram of λ that are direct...