A Study of Some Different Concepts of Symmetry on the Real Line

Recently, different concepts of symmetry on R ⁺ such as R-symmetry, log-symmetry, and double symmetry are studied. Analogous concepts and their properties of these symmetries on R will be studied in this work. Based on skewing representation and previous studies, characterizations of double symmetry on R will be given. Among others, some interesting examples of the so-called I-symmetry, that is the analogue of log-symmetry on R, will also be presented.     

Some further aspects of the löwner-ordering antitonicity of the moore-penrose inverse

A survey is given of known proofs of the antitonicity of the inverse matrix function for positive definite matrices w.r.t. the Lowner partial ordering, and of the corresponding result for the Moore-Penrose inverse of nonnegative definite matrices [the theorem of Milliken and Akdeniz (1977)]. A short new proof of the latter result is obtained by employing an extremal representation of a nonnegative definite quadratic form. Another proof of this result involving Schur complements is also given, and is seen to be extendable to the case of symmetric (not necessarily nonnegative definite) matrices. A geometrical interpretation of Milliken and Akdeniz's theorem is presented. As an application, the relationship between the concepts of greater (maximum) concentration and smaller (minimum) dispersion is considered for a pair (class) of vector-valued statistics with possibly degenerate distributions.     

Extended BIC for linear regression models with diverging number of relevant features and high or ultra-high feature spaces

In many conventional scientific investigations with high or ultra-high dimensional feature spaces, the relevant features, though sparse, are large in number compared with classical statistical problems, and the magnitude of their effects tapers off. It is reasonable to model the number of relevant features as a diverging sequence when sample size increases. In this paper, we investigate the properties of the extended Bayes information criterion (EBIC) (Chen and Chen, 2008) for feature selection in linear regression models with diverging number of relevant features in high or ultra-high dimensional feature spaces. The selection consistency of the EBIC in this situation is established. The application of EBIC to feature selection is considered in a SCAD cum EBIC procedure. Simulation studies are conducted to demonstrate the performance of the SCAD cum EBIC procedure in finite sample cases.     

Bank Business Models at Zero Interest Rates

We propose a novel observation-driven finite mixture model for the study of banking data. The model accommodates time-varying component means and covariance matrices, normal and Student’s t distributed mixtures, and economic determinants of time-varying parameters. Monte Carlo experiments suggest that units of interest can be classified reliably into distinct components in a variety of settings. In an empirical study of 208 European banks between 2008Q1–2015Q4, we identify six business model components and discuss how their properties evolve over time. Changes in the yield curve predict changes in average business model characteristics.     

Locally optimal invariant tests for change in level

The classical change point problem is considered, from the invariance point of view. Locally optimal invariant tests are derived for the change in level, when the initial level and the common variance are assumed to be unknown. The tests derived by Chernoff and Zacks (1964) and Gardner (1969), for the change in level, when variance is known, are shown to be locally optimal invariant tests.     

Discrete Multicolour Random Mosaics with an Application to Network Extraction

We introduce a class of random fields that can be understood as discrete versions of multicolour polygonal fields built on regular linear tessellations. We focus first on a subclass of consistent polygonal fields, for which we show Markovianity and solvability by means of a dynamic representation. This representation is used to design new sampling techniques for Gibbsian modifications of such fields, a class which covers lattice‐based random fields. A flux‐based modification is applied to the extraction of the field tracks network from a Synthetic Aperture Radar image of a rural area.     

日语“空间性状”的时间映射制约研究

日语空间性状的时间映射具有局部映射性和选择性，映射具有负向语义选择偏好；形成“水平线性空间>垂直线性空间>立体三维空间”维度制约等级。上述制约特质是时空隐喻概念相似性与语言类型特质共同驱动促成的。概念相似性是其内在驱动力，相似者易于映射，反之则受制约性强；日语的时间性特质是其负向语义选择偏好的外在驱动力。     

Mapping Right-Wing Women’s Policy Priorities in Latin America

ABSTRACT

Do right-wing women hold unique policy priorities from that of left-wing women and right-wing men? And do right-wing women legislators represent the priorities of right-wing citizens? Right-wing women share unique gendered socialization experiences with left-wing women, but their ideology informs values and attitudes critical to policy preference formation. Political representation theories suggest that women legislators should hold distinct incentives to represent female constituents. However, institutional theories suggest right-wing women legislators may face different incentives that limit the extent to which they represent right-wing female constituents. To evaluate our expectations, we leverage survey data from the Latin American Public Opinion Project and the Parliamentary Elites of Latin America. We demonstrate how right-wing women citizens differ from left-wing women citizens across a range of policy priorities. Then, we evaluate elite priorities for these same policy issues. We find little evidence for policy priority congruency between women citizens and women legislators on the right.     

论适应性表征及其方法论意义

适应性是主体适应其环境的特性,是物理演化系统和生物演化系统的本质属性,反映在认知上就是适应性表征。适应性表征也因此成为知识显现的方式和创造的核心,具有协调性、匹配性、互补性、模拟性和类比性,其表现方式有直接具象表征、间接具象表征、直接抽象表征和间接抽象表征,分别对应于经验主义、建构经验主义、理性主义和科学实在论。适应性表征的实现是通过科学理论核心概念的变化、定律的凝练、理论的更替、模型推理和世界观的改变展开的,具有经验上的适当性。这种经验适当性不仅是感知层次的体验,更是一种认知模式。在认知意义上,经验也是基于心理模型的,心理建模的路径有思想语言、心理表象、心理命题、思想实验和心理模拟推理。这种基于心理建模的适应性表征为科学认知和科学发现提供了有益的方法论。     

Geometric consistency of principal component scores for high-dimensional mixture models and its application

In this article, we consider clustering based on principal component analysis (PCA) for high-dimensional mixture models. We present theoretical reasons why PCA is effective for clustering high-dimensional data. First, we derive a geometric representation of high-dimension, low-sample-size (HDLSS) data taken from a two-class mixture model. With the help of the geometric representation, we give geometric consistency properties of sample principal component scores in the HDLSS context. We develop ideas of the geometric representation and provide geometric consistency properties for multiclass mixture models. We show that PCA can cluster HDLSS data under certain conditions in a surprisingly explicit way. Finally, we demonstrate the performance of the clustering using gene expression datasets.