Composite hierachical linear quantile regression

Multilevel （hierarchical） modeling is a generalization of linear and generalized linear modeling in which regression coefficients are modeled through a model, whose parameters are also estimated from data. Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance （like Cauchy distribution） tends to infinity. This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression, which greatly improves the efficiency and precision of the estimation. The new approach, which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models, still works well when the error variance tends to infinity, We show that even the error distribution is normal, the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression. When the error distribution is not normal, our method still enjoys great advantages in terms of estimation efficiency.     

Fast Inference for the Latent Space Network Model Using a Case-Control Approximate Likelihood

Multilevel modeling is a popular statistical technique for analyzing data in hierarchical format, and thus naturally fits within a distributed database framework. We consider the computational aspects of multilevel modeling across distributed databases. In addition, we consider these aspects under a generalization of the multilevel model where the distributed groups (or databases) are allowed to specify different models at both level-1 (individual) and level-2 (group). For a variety of scenarios, we develop the distributed computation algorithm for two-step least squares (LS) estimators and also for iterative MLE estimators of the parameters of interest; in particular, we determine the required data structure at each computing site, the necessary information (original data, cross-product matrices, coefficient vectors), and the order in which such information needs to be passed between sites. Finally, we discuss recursive updating, fault tolerance, and security issues.     

多变量整体模式累加多层统计模型的建立及其在组织绩效预测上的应用研究

为了解决多层的少样本或无规则数据的建模问题,在一般多层统计模型的基础上提出了多变量整体模式的累加多层统计模型。此模型把累加方法的优点(将无规则数据转化成有规则数据)与多层统计模型结合起来,拓展了多层统计模型的适用范围。从其在香蕉组织绩效的分析以及在仅有两个调查数据香蕉组织形式绩效的预测中,可以看出此模型有较强的实用性。     

Fuzzy systems based on component software

This paper describes hierarchical modeling of fuzzy logic concepts that has been used within the recently developed model of intelligent systems, called OBOA. The model is based on a multilevel, hierarchical, general object-oriented approach. Current methods and software design and development tools for intelligent systems are usually difficult to extend, and it is not easy to reuse their components in developing intelligent systems. The OBOA model tries to reduce these deficiencies. The model starts with a well-founded software engineering principle, making clear distinction between generic, low-level intelligent software components, and domain-dependent, high-level components of an intelligent system. This paper concentrates on modeling and implementation of fuzzy logic concepts within the hierarchical levels of the OBOA model. The fuzzy components described are extensible and adjustable. As an illustration of how these components are used in practice, a practical design example from the domain of medical diagnosis is shown. The paper also suggests some steps towards future design of fuzzy components and tools for intelligent systems.     

物质资本、人力资本、就业结构与西部民族地区农户收入增长

本文基于西部少数民族地区农户收入的微观数据,探讨了利用多水平模型分析具有分层结构数据的统计建模和估计问题,并从物质资本、人力资本、就业结构三个方面研究了影响农村农户收入及其增长的因素及其特征。通过对所得结果的分析,提出了西部少数民族地区农村经济发展的相关政策建议。     

Polynomial extensions of distributions and their applications in actuarial and financial modeling

The paper deals with orthogonal polynomials as a useful technique which can be attracted to actuarial and financial modeling. We use Pearson’s differential equation as a way for orthogonal polynomials construction and solution. The generalized Rodrigues formula is used for this goal. Deriving the weight function of the differential equation, we use it as a basic distribution density of variables like financial asset returns or insurance claim sizes. In this general setting, we derive explicit formulas for option prices as well as for insurance premiums. The numerical analysis shows that our new models provide a better fit than some previous actuarial and financial models.     

基于多维面板数据的聚类方法探析及实证研究

面板数据由于能够从截面和时间构成的二维空间来描述研究对象的动态特征而被广泛应用于经济问题的建模实践中。本文借鉴多元统计学中主成分分析方法对面板数据进行降维处理,然后通过构建综合评价函数序列矩阵的相似指标对面板数据进行聚类分析,并提出一些研究面板数据亲疏关系的有效途径,最后运用该算法对我国地区科技能力进行实证分析,结果与实际状况较为吻合.     

Optimum parameters of hierarchical control structures

The use of multilevel hierarchical structures to effectively conduct inspections and control corruption under the conditions of a shortage of authorized representatives is proposed. Game theory models of such structures are considered and the problem of their organization is reviewed. The optimum strategy for checking in a hierarchy is determined. The results from numerical modeling for the example of taxation of small businesses are given.     

Hierarchical linear regression models for conditional quantiles

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models, but it cannot deal effectively with the data with a hierarchical structure. In practice, the existence of such data hierarchies is neither accidental nor ignorable, it is a common phenomenon. To ignore this hierarchical data structure risks overlooking the importance of group effects, and may also render many of the traditional statistical analysis techniques used for studying data relationships invalid. On the other hand, the hierarchical models take a hierarchical data structure into account and have also many applications in statistics, ranging from overdispersion to constructing min-max estimators. However, the hierarchical models are virtually the mean regression, therefore, they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional covariates. Furthermore, the estimated coefficient vector (marginal effects) is sensitive to an outlier observation on the dependent variable. In this article, a new approach, which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models, is developed. On the theoretical front, we also consider the asymptotic properties of the new method, obtaining the simple conditions for an n1/2-convergence and an asymptotic normality. We also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.     

Some issues in improving quality of noisy periodic signals and estimating their parameters and characteristics numerically by using a cluster approach: Problem statement

In this paper, a technique is proposed to process and analyze noisy periodic signals recorded at discrete moments of time. The technique includes two stages: (a) signal quality improvement (processing) with the use of weighted order statistics filters, and (b) cluster analysis of processing results. Basic definitions and specific features of this type of filtration are given, as well as formulations and definitions of cluster analysis, which enable problems to be stated for periodic signal analysis. The efficiency of cluster analysis with weighted order statistics filters is proved based on results of numerical modeling of a noisy frequency-modulated signal.     

A hierarchical clustering scheme approach to assessment of IP-network traffic using detrended fluctuation analysis

This paper presents an approach to the assessment of IP-network traffic in terms of the time variation of self-similarity. To get a comprehensive view in analyzing the degree of long-range dependence (LRD) of IP-network traffic, we use a hierarchical clustering scheme, which provides a way to classify high-dimensional data with a tree-like structure. Also, in the LRD-based analysis, we employ detrended fluctuation analysis (DFA), which is applicable to the analysis of long-range power-law correlations or LRD in non-stationary time-series signals. Based on sequential measurements of IP-network traffic at two locations, this paper derives corresponding values for the LRD-related parameter α that reflects the degree of LRD of measured data. In performing the hierarchical clustering scheme, we use three parameters: the α value, average throughput, and the proportion of network traffic that exceeds 80% of network bandwidth for each measured data set. We visually confirm that the traffic data can be classified in accordance with the network traffic properties, resulting in that the combined depiction of the LRD and other factors can give us an effective assessment of network conditions at different times.     

Asymptotic models and inference for extremes of spatio-temporal data

Recently there has been a lot of effort to model extremes of spatially dependent data. These efforts seem to be divided into two distinct groups: the study of max-stable processes, together with the development of statistical models within this framework; the use of more pragmatic, flexible models using Bayesian hierarchical models (BHM) and simulation based inference techniques. Each modeling strategy has its strong and weak points. While max-stable models capture the local behavior of spatial extremes correctly, hierarchical models based on the conditional independence assumption, lack the asymptotic arguments the max-stable models enjoy. On the other hand, they are very flexible in allowing the introduction of physical plausibility into the model. When the objective of the data analysis is to estimate return levels or kriging of extreme values in space, capturing the correct dependence structure between the extremes is crucial and max-stable processes are better suited for these purposes. However when the primary interest is to explain the sources of variation in extreme events Bayesian hierarchical modeling is a very flexible tool due to the ease with which random effects are incorporated in the model. In this paper we model a data set on Portuguese wildfires to show the flexibility of BHM in incorporating spatial dependencies acting at different resolutions.     

A multilevel approach for nonnegative matrix factorization

Nonnegative matrix factorization (NMF), the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices, has been shown to be useful in many applications, such as text mining, image processing, and computational biology. In this paper, we explain how algorithms for NMF can be embedded into the framework of multilevel methods in order to accelerate their initial convergence. This technique can be applied in situations where data admit a good approximate representation in a lower dimensional space through linear transformations preserving nonnegativity. Several simple multilevel strategies are described and are experimentally shown to speed up significantly three popular NMF algorithms (alternating nonnegative least squares, multiplicative updates and hierarchical alternating least squares) on several standard image datasets.     

A multilevel successive iteration method for nonlinear elliptic problems

In this paper, a multilevel successive iteration method for solving nonlinear elliptic problems is proposed by combining a multilevel linearization technique and the cascadic multigrid approach. The error analysis and the complexity analysis for the proposed method are carried out based on the two-grid theory and its multilevel extension. A superconvergence result for the multilevel linearization algorithm is established, which, besides being interesting for its own sake, enables us to obtain the error estimates for the multilevel successive iteration method. The optimal complexity is established for nonlinear elliptic problems in 2-D provided that the number of grid levels is fixed.

     

Analysis of decomposition algorithms via nonlinear splitting functions

This paper provides a structural analysis of decomposition algorithms using a generalization of linear splitting methods. This technique is used to identify explicitly the essential similarities and differences between several classical algorithms. Similar concepts can be used to analyze a large class of multilevel hierarchical structures.This research was supported in part by ONR Contract No. N00014-76-C-0346, in part by the US Department of Energy, Division of Electric Energy Systems, Contract No. ERDA-E(49-18)-2087 at the Massachusetts Institute of Technology, and in part by the Joint Services Electronics Program, Contract No. DAAG-29-78-C-0016.The authors would like to thank Dr. P. Varaiya, University of California at Berkeley, and Dr. D. Bertsekas for their comments and suggestions.     

Fuzzy measure analysis of public attitude towards the use of nuclear energy

This paper is concerned with applying fuzzy measures and fuzzy integrals to analyze public attitude towards the use of nuclear energy. To this end, a questionnaire on the use of nuclear energy is set up and data are collected in Japan, the Philippines and the FRG. Factor analysis is performed to get the primary structure of public attitude. It is shown that the attitude of the responders to the questionnaire in each country is well explained with its hierarchical structure obtained by fuzzy measure analysis.     

An isogeometric boundary element approach for topology optimization using the level set method

Among the various types of structural optimization, topology has been occupying a prominent place over the last decades. It is considered the most versatile because it allows structural geometry to be determined taking into account only loading and fixing constraints. This technique is extremely useful in the design phase, which requires increasingly complex computational modeling. Modern geometric modeling techniques are increasingly focused on the use of NURBS basis functions. Consequently, it seems natural that topology optimization techniques also use this basis in order to improve computational performance. In this paper, we propose a way to integrate the isogeometric boundary techniques to topology optimization through the level set function. The proposed coupling occurs by describing the normal velocity field from the level set equation as a function of the normal shape sensitivity. This process is not well behaved in general, so some regularization technique needs to be specified. Limiting to plane linear elasticity cases, the numerical investigations proposed in this study indicate that this type of coupling allows to obtain results congruent with the current literature. Moreover, the additional computational costs are small compared to classical techniques, which makes their advantage for optimization purposes evident, particularly for boundary element method practitioners.     

Robust semi-coarsening multilevel preconditioning of biquadratic FEM systems

While a large amount of papers are dealing with robust multilevel methods and algorithms for linear FEM elliptic systems, the related higher order FEM problems are much less studied. Moreover, we know that the standard hierarchical basis two-level splittings deteriorate for strongly anisotropic problems. A first robust multilevel preconditioner for higher order FEM systems obtained after discretizations of elliptic problems with an anisotropic diffusion tensor is presented in this paper. We study the behavior of the constant in the strengthened CBS inequality for semi-coarsening mesh refinement which is a quality measure for hierarchical two-level splittings of the considered biquadratic FEM stiffness matrices. The presented new theoretical estimates are confirmed by numerically computed CBS constants for a rich set of parameters (coarsening factor and anisotropy ratio). In the paper we consider also the problem of solving efficiently systems with the pivot block matrices arising in the hierarchical basis two-level splittings. Combining the proven uniform estimates with the theory of the Algebraic MultiLevel Iteration (AMLI) methods we obtain an optimal order multilevel algorithm whose total computational cost is proportional to the size of the discrete problem with a proportionality constant independent of the anisotropy ratio.     

Hierarchical mixture models for zero-inflated correlated count data

Count data with excess zeros are often encountered in many medical, biomedical and public health applications. In this paper, an extension of zero-inflated Poisson mixed regression models is presented for dealing with multilevel data set, referred as hierarchical mixture zero-inflated Poisson mixed regression models. A stochastic EM algorithm is developed for obtaining the ML estimates of interested parameters and a model comparison is also considered for comparing models with different latent classes through BIC criterion. An application to the analysis of count data from a Shanghai Adolescence Fitness Survey and a simulation study illustrate the usefulness and effectiveness of our methodologies.     

基于EM算法的混合模型中子总体个数的研究

混合模型已成为数据分析中最流行的技术之一,由于拥有数学模型,它通常比聚类分析中的传统的方法产生的结果更精确,而关键因素是混合模型中子总体个数,它决定了数据分析的最终结果。期望最大化(EM)算法常用在混合模型的参数估计,以及机器学习和聚类领域中的参数估计中,是一种从不完全数据或者是有缺失值的数据中求解参数极大似然估计的迭代算法。学者们往往采用AIC和BIC的方法来确定子总体的个数,而这两种方法在实际的应用中的效果并不稳定,甚至可能会产生错误的结果。针对此问题,本文提出了一种利用似然函数的碎石图来确定混合模型中子总体的个数的新方法。实验结果表明,本文方法确定的子总体的个数在大部分理想的情况下可以得到与AIC、BIC方法确定的聚类个数相同的结果,而在一般的实际数据中或条件不理想的状态下,碎石图方法也可以得到更可靠的结果。随后,本文将新方法在选取的黄石公园喷泉数据的参数估计中进行了实际的应用。