Importance measures have been widely studied and applied in reliability and safety engineering. This paper presents a general formulation of moment-independent importance measures and several commonly discussed importance measures are unified based on Minkowski distance (MD). Moment-independent importance measures can be categorized into three classes of MD importance measures, i.e. probability...

This paper attempts to introduce the concept of moment invariance into the classification algorithm based on the morphological boundary extraction and generalized skeleton transform, and tries to propose a new method about shape classification in this field. Firstly, the method extracts boundary of the object, secondly, skeleton using main skeleton extraction algorithm based on visual important...

In this paper we present a universal solution to the generalized moment problem, with a nonclassical complexity constraint. We show that this solution can be obtained by minimizing a strictly convex nonlinear functional. This optimization problem is derived in two different ways. We first derive this intrinsically, in a geometric way, by path integration of a one-form which defines the generali...

The main approach to handle endogeneity in econometrics has been instrumental variable estimator (IVE). An instrument m requires E(mu) = 0 where u is an error term, and if E(mu) 6= 0 is likely, then m gets discarded. But when E(mu) 6= 0, fairly often one has a good idea on the sign of E(mu), and it will be a waste to toss out the sign information. This paper shows how to make use of the informa...

High-order Hu moment invariant functions have always been required to solve a variety of problems. Up to this point, there was no generalized approach to extend the first six Hu moment invariants to higher orders. Therefore, this paper presents a generalized algorithm to determine rotationally invariant Hu moment invariants of any desired order, which are invariant to scaling, translation and r...

We present a semi-parametric method for testing mixing distributions in the mixed Poisson model. The proposed method, which is based on the generalized method of moments, does not demand the complete specification of the probability function but only requires a specification of a set of moment conditions which the model should satisfy. We demonstrate that an explicit expression for moment relat...

Using the language of exponential Riordan arrays, we study three distinct families of orthogonal polynomials defined by trigonometric functions. We study the moment sequences of theses families, finding continued fraction expressions for their generating functions, and calculate the Hankel transforms of these moment sequences. Results related to the Euler or zigzag numbers, as well as the gener...

Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification. In this paper, we apply the framework of M-estimation to develop both a generalized method of moments procedure and a principled method for regularization. O...

M. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kähler manifold preserved by the complexification of the Hamiltonian group action. V. Guillemin and R. Sjamaar generalized this result to irreducible subvarieties preserved only by a Borel subgroup. In another direction, L. O’Shea and R. Sjamaar proved a convexity result for the moment...

In this paper, we show that the notion of moment map for the Hamiltonian action of a Lie group on a symplectic manifold is a special case of a much more general notion. In particular, we show that one can associate a moment map to a family of Hamiltonian symplectomorphisms, and we prove that its image is characterized, as in the classical case, by a generalized “energy-period” relation.