Estimation of a tail index based on minimum density power divergence

In this paper, we consider the minimum density power divergence estimator for the tail index of heavy tailed distributions in strong mixing processes. It is shown that the estimator is consistent and asymptotically normal under regularity conditions. The simulation results demonstrate that the estimator is robust in the presence of outliers.     

A class of weighted multivariate normal distributions and its properties

This article proposes a class of weighted multivariate normal distributions whose probability density function has the form of a product of a multivariate normal density and a weighting function. The class is obtained from marginal distributions of various doubly truncated multivariate normal distributions. The class strictly includes the multivariate normal and multivariate skew-normal. It is useful for selection modeling and inequality constrained normal mean vector analysis. We report on a study of some distributional properties and the Bayesian perspective of the class. A probabilistic representation of the distributions is also given. The representation is shown to be straightforward to specify the distribution and to implement computation, with output readily adapted for the required analysis. Necessary theories and illustrative examples are provided.     

Cauchy problem for a class of degenerate kolmogorov-type parabolic equations with nonpositive genus

We study the properties of the fundamental solution and establish the correct solvability of the Cauchy problem for a class of degenerate Kolmogorov-type equations with { p^?,h^? } \left\{ {\overrightarrow p, \overrightarrow h } \right\} -parabolic part with respect to the main group of variables and nonpositive vector genus in the case where the solutions are infinitely differentiable functions and their initial values are generalized functions in the form of Gevrey ultradistributions.     

Classification of a screened data into one of two normal populations perturbed by a screening scheme

In normal classification analysis, there may be cases where the population distributions are perturbed by a screening scheme. This paper considers a new classification method for screened data that is obtained from the perturbed normal distributions. Properties of each population distribution is considered and the best region for classifying the screened data is obtained. These developments yield yet another optimal rule for the classification. The rule is studied from several aspects such as a linear approximation, error rates, and estimation of the rule using the EM algorithm. Relationships among these aspects as well as investigation of the rule’s performance are also considered. The screened classification ideas are illustrated in detail using numerical examples.     

Equivariant cohomology distinguishes the geometric structures of toric hyperkähler manifolds

Toric hyperkähler manifolds are the hyperkähler analogue of symplectic toric manifolds. The theory of Bielawski and Dancer tells us that, while a symplectic toric manifold is determined by a Delzant polytope, a toric hyperkähler manifold is determined by a smooth hyperplane arrangement. The purpose of this paper is to show that a toric hyperkähler manifold up to weak hyperhamiltonian T -isometry is determined not only by a smooth hyperplane arrangement up to weak linear equivalence but also by its equivariant cohomology H* _T (M; ?) with a point â in H ²(M;?) \ {0} up to weak H*(BT; ?)-algebra isomorphism preserving â.     

Rigidity problems in toric topology: A survey

Several rigidity problems in toric topology are addressed in the survey paper by the second and third authors, “Classification Problems of Toric Manifolds via Topology” (in Toric Topology, Am. Math. Soc., Providence, RI, 2008, pp. 273–286). In the present paper, we survey the results on those problems including recent developments.     

Extremal graph characterization from the bounds of the spectral radius of weighted graphs

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained.     

Comparison results of the preconditioned AOR methods for L-matrices

In this paper, we first provide comparison results of several types of the preconditioned AOR (PAOR) methods for solving a linear system whose coefficient matrix is an L-matrix satisfying some weaker conditions than those used in the recent literature. Next, we propose an application of PAOR method to a preconditioner of Krylov subspace method. Lastly, numerical results are provided to show that Krylov subspace method with the PAOR preconditioner performs quite well as compared with the ILU (0) preconditioner.     

Optimal investment and consumption decision of a family with life insurance

We study an optimal portfolio and consumption choice problem of a family that combines life insurance for parents who receive deterministic labor income until the fixed time T. We consider utility functions of parents and children separately and assume that parents have an uncertain lifetime. If parents die before time T, children have no labor income and they choose the optimal consumption and portfolio with remaining wealth and life insurance benefit. The object of the family is to maximize the weighted average of utility of parents and that of children. We obtain analytic solutions for the value function and the optimal policies, and then analyze how the changes of the weight of the parents’ utility function and other factors affect the optimal policies.