Approximation Multivariate Distribution with Pair Copula Using the Orthonormal Polynomial and Legendre Multiwavelets Basis Functions

We concentrate on constructing higher dimensional distributions using a fast growing graphical model called Vine/ pair-copula model which has been introduced and developed by Joe, Cooke, Bedford, Kurowica, Daneshkhah, and others. They first construct a n-dimensional copula density by stacking together n(n ? 1)/2 bivariate copula density, and they then approximate arbitrarily well these bivariate copulas and the corresponding multivariate distribution using a semi-parametric method. One constructive approach involves the use of minimum information copulas that can be specified to any required degree of precision based on the available data (or possibly based on the experts’ judgments). By using this method, one is able to use a fixed finite dimensional family of copulas to be employed in terms of a vine construction, with the promise of a uniform level of approximation.

The basic idea behind this method is to use a two-dimensional ordinary polynomial series to approximate any log-density of a bivariate copula function by truncating the series at an appropriate point. We make this approximation method more accurate and computationally faster by using the orthonormal polynomial and Legendre multiwavelets (LMW) series as the basis functions. We show the derived approximations are more precise and computationally faster with better properties than the one proposed previous method in the literature. We then apply our method to modeling a dataset of Norwegian financial data that was previously analyzed in the series of articles, and finally compare our results by them. At the end, we present a method to simulate from the approximated models, and validate our approximation using the simulation results to recover the same dependency structure of the original data.     

结构功能主义视角下乡村旅游的可持续发展

乡村旅游的管理结构可以视为具有一定结构的系统,要维持该系统的有效运行,政府、投资经营者以及当地村民应该发挥既有的功能。近年来我国乡村旅游产业发展速度虽然很快,但也存在着政府未充分发挥社会治理职能、投资经营者对乡村旅游可持续发展的认识较浅显、当地村民缺乏相关专业知识且缺失话语权等一些不容忽视的矛盾和问题,直接影响了乡村旅游的可持续发展。为了促进我国乡村旅游的可持续发展,政府应设立专项资金,吸引投资并进行科学规划与规范管理;投资经营者应深入挖掘特色乡土文化,同时构建并延伸产业链;村民应该积极参加专业培训,增强自身参与性。     

How to beat early movers: The role of competitive strategy and industry dynamism on followers’ performance in the telecommunications industry

The idea of first-mover advantages is frequently used by both managers and academics alike. Despite its importance for understanding the performance of entry in new markets, the evidence remains mixed. Our study advances research on the entry timing-performance relationship by adopting a contingency perspective that includes both micro (competitive strategies) and macro (industry dynamics) dimensions to explain differences in entrants' profitability. In this paper we focus on follower firms and propose that cost leadership is the best strategy for them to successfully entering a market. In addition, recognizing the contingency effect of industry dynamism, we also examine how market growth and technology evolution affect the effectiveness of followers’ competitive strategies. Specifically, we propose that followers will be better off by using cost strategies in growing markets, while when operating in contexts of technological change the performance of the cost leadership strategy will be lower.     

我国专业市场现状及改造提升前景——基于对某县级市S专业市场调查的分析与研究

专业市场经过多年的发展,竞争日益激烈,在新形势下各种矛盾逐渐显露,已经进入整合、分化、转型升级阶段,改造提升迫在眉睫。通过对某市专业市场经营户经营状况以及市场布局、管理水平、市场在当地知名度和美誉度等的调查结果的分析研究,有助于形成专业市场改造提升的方向、目标和整体思路。     

Fitting models to data: Interaction versus polynomial? your choice

Polynomials are widely used for fitting models empirically to data. Low-degree polynomials (specifically, degrees 1, 2, and at most 3) have stood the test of time by proving their versatility when it comes to fitting a wide variety of different surface shapes over limited regions of interest. However, when faced with modeling a surface over an experimental region whose boundaries extend beyond some localized neighborhood or limited-sized region of interest, a polynomial of degree 2, or even of degree 3, may not be adequate. For this situation we propose fitting an interaction model which is a reduced form of higher-degree polynomial. Some examples of actual experiments are presented to illustrate the improvement in fit by an interaction model over that of a standard polynomial, even for response surfaces with uncomplicated shapes.     

Asymptotic normality for limiting discrete distributions

Three basic asymptotic normality conditions for limiting discrete distributions are given in terms of differencing operators. Under these conditions one can establish asymptotic normality by directly dealing with the limiting behaviors of distribution functions themselves without resorting to the central limit theorem.     

Minimum Cost Edge Subset Covering Exactly k Vertices of a Graph

Given a graph G with nonnegative edge costs and an integer k, we consider the problem of finding an edge subset S of minimum total cost with respect to the constraint that S covers exactly k vertices of G. An O(n ³) algorithm is presented where n is the order of G. It is based on the author's previous paper dealing with a similar problem asking S to cover at least k vertices.     

A-optimal designs for mixture central polynomial model with qualitative factors

Mixture central polynomial models with qualitative factors are widely applied in many fields of research. In this paper, a method of finding A-optimal design for two degree mixture central polynomial model with qualitative factors will be proposed. The variance function will be given for getting the support points of the design. The A-optimality is confirmed by the equivalence theorem. In addition, this method also works effectively with higher degree models.     

On the distribution of a second degree polynomial statistic in singular normal var1aies

This note provides an alternative proof of a basic theorem on the distribution of a second degree polynomial statistic in noncentral singular normal variates originally proven by Rayner and Livingstone (1965)     

Recurrence relations of coefficients of the generalized hypergeometric function in multivariate analysis

James(1960) defined the zonal polynomials and used it to represent the joint distributions of latent roots of VVisfiart matrix. The zonal polviionnals played an important role to define the generalized hypergeometric function of symmetric matrix argument Since then, many density functions and moments based on Wishart matrix have been expressed in terms of the generalized hy¬pergeometric Function. The purpose of this paper is to get the recurrence relations for the coefficients of it. In Section 1 we derive a partial differen¬tial equations having the generalized hypergeometric function as the unique solution. Then we ubtain the recurrence relations until order 7 in Section 2.