中国股市基本面价值加权投资组合研究

基本面价值加权投资组合是近年来在美国兴起的新型投资理论和技术.其基础是噪声市场假说和价格回归价值。本文回顾了基本面投资组合的相关文献,解释了其建立的理论基础和模型.本文还根据平滑市值权重技术,构建了基于中国股票市场的基本面投资组合,并和传统的市值加权投资组合进行比较。本文的主要结论是,中国市场1992年到2002年和美国市场类似呈现平稳价格噪声,基本面投资组合总体优于市值加权组合.股权分置改革初期市场低落,市场价格过度低估基本面价值,市值组合占优势。2005年下半年来股市呈现一定泡沫特征,市场价格对基本面价值有过度高估趋势,间接地证明了相关部门对股市过热的警告和监管是合理的.     

Small generators of the ideal class group

Assuming the Generalized Riemann Hypothesis, Bach has shown that the ideal class group of a number field can be generated by the prime ideals of having norm smaller than . This result is essential for the computation of the class group and units of by Buchmann's algorithm, currently the fastest known. However, once has been computed, one notices that this bound could have been replaced by a much smaller value, and so much work could have been saved. We introduce here a short algorithm which allows us to reduce Bach's bound substantially, usually by a factor 20 or so. The bound produced by the algorithm is asymptotically worse than Bach's, but favorable constants make it useful in practice.

     

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Homogeneity of variance and correlation coefficients is one of assumptions in the analysis of longitudinal data.However, the assumption can be challenged. In this paper, we mainly propose and analyze nonlinear mixed effects models for longitudinal data with exponential correlation covariance structure, intend to introduce Huber's function in the log likelihood function and get robust estimation (M-estimation) by Fisher scoring method. Score test statistics for homogeneity of variance and correlation coefficient based on M-estimation are then studied. A simulation study is carried to assess the performance of test statistics and the method we proposed in the paper is illustrated by an actual data example.     

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With the advance of computer storage capacity and online observation technique, more and more data are collected with curves and images. The most two important feature of curve and image data are high-dimension and high correlation between adjacent data. Functional data analysis has more advantage in deal with these data, which can not be treated by traditional multivariate statistics methods. Recently, a variety of functional data methods have been developed, including curve alignment, principal component analysis, regression, classification and clustering. In this paper, we mainly introduce the origins,development and recent process of functional data. Specifically, we firstly introduce the notion of functional data. Secondly, functional principal component analysis has been presented. Then, this paper is devoted to introduce estimation, variable selection and hypothesis testing of functional regression models. Lastly, the paper concludes with a brief discussion of future directions.     

函数型数据回归分析综述

随着计算机储存能力和在线观测技术的提高,当今数据越来越多的以曲线和图像的形式存在.曲线和图像数据两个最显著的特征是高维和相邻数据间高度相关.这些特征使得传统的多元统计分析方法不再适合,而函数型数据在处理曲线和图像数据中具有无可比拟的优势.近年来各种各样的函数型数据分析方法得以发展,其中包括数据的对齐、主成分分析、回归、分类、聚类等.本文主要介绍函数型数据回归分析研究的起源、发展及最新进展.具体地,本文首先介绍函数型数据的概念;其次介绍函数型主成分分析方法;再次着重介绍函数型回归模型的估计、变量选择和检验方法;最后将简要探讨函数型数据未来的可能发展方向.     

具有遗传性疾病和性状的遗传位点分析

随着信息技术的进步和发展,现代生物学越来越多地将这些技术用于大规模生物数据的收集、分析、挖掘等过程.大量计算机技术,特别是统计方法被用来进行复杂疾病的分析.大量研究表明,人体的许多表型性状差异以及对药物和疾病的易感性等都可能与某些位点相关联,或和包含有多个位点的基因相关联.因此,定位与性状或疾病相关联的位点在染色体或基因中的位置,能帮助研究人员了解性状和一些疾病的遗传机理,也能使人们对致病位点加以干预,防止一些遗传病的发生.利用随机森林方法、Bootstrap重抽样、logistic回归等大数据分析方法,意在解决优化生物学位点关联性分析中单一致病位点识别、多位点相互作用和多性状位点关联性分析等子问题.     

A Convergence Analysis of Newton-Like Method for Singular Equations Using Recurrent Functions

We provide new semilocal convergence results for Newton-like method involving outer or generalized inverses in a Banach space setting. Using our new idea of recurrent functions and the same or weaker conditions than before [5-19 A. Ben-Israel and N.E. Greville ( 1974 ). Generalized Inverses: Theory and Applications, Pure and Applied Mathematics . Wiley-Interscience , New York . X. Chen and T. Yamamoto ( 1989 ). Convergence domains of certain iterative methods for solving nonlinear equations . Numer. Funct. Anal. Optimiz. 10 : 37 – 48 . J.E. Dennis , Jr. ( 1968 ). On Newton-like methods . Numer. Math. 11 : 324 – 330 . P. Deuflhard and C. Heindl ( 1979 ). Convergence theorems for Newton's method and extensions to related methods . SIAM J. Numer. Anal. 16 : 1 – 10 . J.M. Gutiérrez ( 1997 ). A new semilocal convergence theorem for Newton's method . J. Comp. Appl. Math. 79 : 131 – 145 . J.M. Gutiérrez , M.A. Hernández , and M.A. Salanova ( 1995 ). Accessibility of solutions by Newton's method . Internat. J. Comput. Math. 57 : 239 – 247 . W.M. Häubler ( 1986 ). A Kantorovich-type convergence analysis for the Gauss–Newton methods . Numer. Math. 48 : 119 – 125 . L.V. Kantorovich and G.P. Akilov ( 1964 ). Functional Analysis . Pergamon Press , Oxford . M.Z. Nashed and X. Chen ( 1993 ). Convergence of Newton-like methods for singular operator equations using outer inverses . Numer. Math. 66 : 235 – 257 . F.A. Potra and V. Ptàk ( 1980 ). Sharp error bounds for Newton's process . Numer. Math. 34 : 67 – 72 . W.C. Rheinboldt ( 1968 ). A unified convergence theory for a class of iterative processes . SIAM J. Numer. Anal. 5 : 42 – 63 . W.C. Rheinboldt ( 1977 ). An adaptive continuation process for solving systems of nonlinear equations . Polish Academy of Sciences, Banach Ctr. Publ. 3 : 129 – 142 . T. Yamamoto ( 1987 ). A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions . Numer. Math. 49 : 203 – 230 . T. Yamamoto ( 1987 ). A convergence theorem for Newton-like methods in Banach spaces . Numer. Math. 51 : 545 – 557 . T. Yamamoto ( 1989 ). Uniqueness of the solution in a Kantorovich-type theorem of Haubler for the Gauss–Newton method . Japan J. Appl. Math. 6 : 77 – 81 . ], we provide more precise information on the location of the solution and finer bounds on the distances involved. Moreover, since our Newton–Kantorovich-type hypothesis is weaker than before, we can now cover cases not previously possible.

Applications and numerical examples involving a nonlinear integral equation of Chandrasekhar-type and a differential equation with Green's function are also provided in this study.     

Large Deviation Probabilities for Square-Gaussian Stochastic Processes

We investigate properties of square-Gaussian stochastic processes. These processes are formed by quadratic forms of Gaussian processes or by limits in the mean square of quadratic forms of Gaussian processes. Special classes of these processes are determined and investigated. For processes from these classes estimates of large deviation probability are obtained. These estimates we use to estimate the probability that Gaussian vector-valued process leave some region on some interval of time. We construct asymptotic confidence regions for estimates of covariance functions of vector-valued Gaussian processes. Criterion of hypothesis testing on covariance functions of these processes is constructed.     

Infinite-dimensional 4-manifold of finite cohomological dimension under the continuum hypothesis

Under the assumption of the continuum hypothesis, a differentiable 4-manifoldM of dimension dimM=∞ and cohomological dimension cA—dimM=4 is constructed. The spaceM is perfectly normal and hereditarily separable. Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 664–670, November, 1999.