Maximum likelihood estimate for discontinuous parameter in stochastic hyperbolic systems

The purpose of this paper is to study the identification problem of a spatially varying discontinuous parameter in stochastic hyperbolic equations. In previous works, the consistency property of the maximum likelihood estimate (MLE) was explored and the generating algorithm for MLE proposed under the condition that an unknown parameter is in a sufficiently regular space with respect to spatial variables.In order to show the consistency property of the MLE for a discontinuous coefficient, we use the method of sieves, i.e. the admissible class of unknown parameters is projected into a finite-dimensional space. For hyperbolic systems, we cannot obtain a regularity property of the solution with respect to a parameter. So in this paper, the parabolic regularization technique is used. The convergence of the derived finite-dimensional MLE to the infinite-dimensional MLE is justified under some conditions.     

Nonstationary curves in Hilbert spaces and their correlation functions II

Partially supportted by Grant MM-22/1991 of MESC     

Optical current transducer with bulk type Bi12SiO20 faraday sensor for power systems

Two types of optical current transducers (OCTs) have a bulk Faraday sensor inserted into the gap of an iron core and a porcelain insulator with optical fiber. The sensor consists of Bi₁₂SiO₂₀ (BSO) single crystal, a polarizer, and an analyzer. The OCTs satisfied the target performance requirement for fault location and metering and demonstrated maintained performance at some power utilities in Japan and the US. We have developed a fault location system that immediately detects the fault current with the OCTs, there by locating the fault section. The OCT can easily replace the existing support insulators for the disconnecting switch without any modifications to structure height or bus-bar. For metering requiring 0.3% class accuracy, use of a BSO with right optical rotatory power combined with BSO with left optical rotatory power results in a Faraday sensor with improved temperature characteristics. The OCT demonstrated 0.3% class accuracy for metering described in the current transformer Specifications of IEEE C57–13, 1993.     

Nonnegative quadratic estimation and quadratic sufficiency in general linear models

Notions of linear sufficiency and quadratic sufficiency are of interest to some authors. In this paper, the problem of nonnegative quadratic estimation for β^′Hβ+hσ² is discussed in a general linear model and its transformed model. The notion of quadratic sufficiency is considered in the sense of generality, and the corresponding necessary and sufficient conditions for the transformation to be quadratically sufficient are investigated. As a direct consequence, the result on (ordinary) quadratic sufficiency is obtained. In addition, we pose a practical problem and extend a special situation to the multivariate case. Moreover, a simulated example is conducted, and applications to a model with compound symmetric covariance matrix are given. Finally, we derive a remark which indicates that our main results could be extended further to the quasi-normal case.     

On the convergence of Newton's method when estimating higher dimensional parameters

In this paper, we consider the estimation of a parameter of interest where the estimator is one of the possibly several solutions of a set of nonlinear empirical equations. Since Newton's method is often used in such a setting to obtain a solution, it is important to know whether the so obtained iteration converges to the locally unique consistent root to the aforementioned parameter of interest. Under some conditions, we show that this is eventually the case when starting the iteration from within a ball about the true parameter whose size does not depend on n. Any preliminary almost surely consistent estimate will eventually lie in such a ball and therefore provides a suitable starting point for large enough n. As examples, we will apply our results in the context of M-estimates, kernel density estimates, as well as minimum distance estimates.     

REML estimation for binary data in GLMMs

The restricted maximum likelihood (REML) procedure is useful for inferences about variance components in mixed linear models. However, its extension to hierarchical generalized linear models (HGLMs) is often hampered by analytically intractable integrals. Numerical integration such as Gauss-Hermite quadrature (GHQ) is generally not recommended when the dimensionality of the integral is high. With binary data various extensions of the REML method have been suggested, but they have had unsatisfactory biases in estimation. In this paper we propose a statistically and computationally efficient REML procedure for the analysis of binary data, which is applicable over a wide class of models and design structures. We propose a bias-correction method for models such as binary matched pairs and discuss how the REML estimating equations for mixed linear models can be modified to implement more general models.     

Asymmetric synthesis of abietane diterpenoids via B-alkyl Suzuki-Miyaura coupling. Formal total asymmetric synthesis of 12-deoxyroyleanone and cryptoquinone

A convergent synthetic strategy for abietane diterpenoids via B-alkyl Suzuki-Miyaura coupling and Lewis acid-mediated cyclization reactions is established. Asymmetric total synthesis of 12-deoxyroyleanone, an antileishmanial diterpene, is described.     

Automorphisms and blocking in simple games

Different (proper as well as improper) simple games may share any nonseparating blocking family. An interesting question is whether all such proper games on one hand, and all improper ones on the other, are isomorphic. The answer is given here and the automorphisms of the blocking family help us to understand the structure and links of all such games.     

Some explicit examples of Hamiltonian minimal Lagrangian submanifolds in complex space forms

In this paper, we find some new explicit examples of Hamiltonian minimal Lagrangian submanifolds among the Lagrangian isometric immersions of a real space form in a complex space form.