Multi-stage nested classification credibility quantile regression model

In insurance (or in finance) practice, in a regression setting, there are cases where the error distribution is not normal and other cases where the set of data is contaminated due to outlier events. In such cases the classical credibility regression models lead to an unsatisfactory behavior of credibility estimators, and it is more appropriate to use quantile regression instead of the ordinary least squares estimation. However, these quantile credibility models cannot perform effectively when the set of data has nested (hierarchical) structure. This paper develops credibility models for regression quantiles with nested classification as an alternative to Norberg’s (1986) approach of random coefficient regression model with multi-stage nested classification. This paper illustrates two types of applications, one with insurance data and one with Fama/French financial data.     

Application of conjugate-gradient-like methods to a hyperbolic problem in porous-media flow

This paper presents the application of a preconditioned conjugate-gradient-like method to a non-self-adjoint problem of interest in underground flow simulation. The method furnishes a reliable iterative solution scheme for the non-symmetric matrices arising at each iteration of the non-linear time-stepping scheme. The method employs a generalized conjugate residual scheme with nested factorization as a preconditioner. Model runs demonstrate significant computational savings over direct sparse matrix solvers.     

On the topology of nested set complexes

Nested set complexes appear as the combinatorial core of De Concini-Procesi arrangement models. We show that nested set complexes are homotopy equivalent to the order complexes of the underlying meet-semilattices without their minimal elements. For atomic semilattices, we consider the realization of nested set complexes by simplicial fans proposed by the first author and Yuzvinsky and we strengthen our previous result showing that in this case nested set complexes in fact are homeomorphic to the mentioned order complexes.

     

Methods for nesting rank 3 normalized matching rank-unimodal posets

Anderson and Griggs proved independently that a rank-symmetric-unimodal normalized matching (NM) poset possesses a nested chain decomposition (or nesting), and Griggs later conjectured that this result still holds if we remove the condition of rank-symmetry. We give several methods for constructing nestings of rank-unimodal NM posets of rank 3, which together produce substantial progress towards the rank 3 case of the Griggs nesting conjecture. In particular, we show that certain nearly symmetric posets are nested; we show that certain highly asymmetric rank 3 NM posets are nested; and we use results on minimal rank 1 NM posets to show that certain other rank 3 NM posets are nested.     

Design of a permanent magnet with a mechanical sweep suitable for variable-temperature continuous-wave and pulsed EPR spectroscopy

A magnetic system is introduced which consists of three nested rings of permanent magnets of a Halbach dipolar layout and is capable for EPR spectroscopy. Two of the rings can be rotated independently to adjust the magnetic flux in the center and even allow for mechanical field sweeps. The presented prototype achieves a magnetic flux range of 0.0282–0.3013 T with a minimal sweep of 0.15 mT and homogeneity of about 10⁻³.First applications with CW and pulsed Mims ENDOR as well as ESEEM experiments on a sample of a glycine single crystal doped with 1% copper nitrate demonstrate that flux range, sweep accuracy and homogeneity of this prototype is sufficient for EPR experiments on most solid samples.Together with a recently improved design magnets can be build which could serve as compact and easily transportable replacement of standard electromagnets with negligible consumption of power or coolants.     

GeneralizedF-tests for unbalanced nested designs under heteroscedasticity

Two-factor fixed-effect unbalanced nested design model without the assumption of equal error variance is considered. Using the generalized definition ofp-values, exact tests under heteroscedasticity are derived for testing main effects of both factors. These generalizedF-tests can be utilized in significance testing or in fixed level testing under the Neyman-Pearson theory. Two examples are given to illustrate the proposed test and to demonstrate its advantages over the classicalF-test. Extensions of the procedure for three-factor nested designs are briefly discussed.     

Fuzzy线性空间与Fuzzy向量

利用集合套给出Fuzzy 线性空间的又一定义,讨论了它的点态刻划,并研究了Fuzzy向量及其线性关系。     

Index to Volume 1 (1992)

Abstract

Since its introduction, APL has frequently been touted as an ideal programming language for statistical applications. Among the attractive features of APL for statistics are its extensibility, the presence of primitives for operations such as sorting, matrix inversion, and arranging data, and powerful facilities for handling matrices and other arrays. Newer programming languages incorporating some of the features of APL—notably New S and XLisp-Stat—have been designed specifically for statistical applications. Is there still a niche for APL?

We believe that APL2 continues to offer some significant benefits for statistical computation, including user-defined operators, nested arrays, and convenient implementation of arrays of any dimension. We use these characteristics of the language in the course of designing an extensible computing environment for data analysis and programming based on APL2 that incorporates some of the features of modern statistical programming languages, such as data objects, symbolic model specification, missing-data handling, and automatic search of a path of files. The system, which includes interactive statistical graphics, general linear models, and robust estimation methods, has been implemented using IBM's APL2 for PC-compatibles—both the standard version of this system and the freeware TryAPL2. The latter provides students with a free environment for modern data analysis and one in which they can explore the design of statistical software.