自回归参数估计的渐近均方误差

近年来时间序列分析中的模型识别和参数估计方法(如[1—3]),得到了广泛的应用与发展。关于参数估计的渐近性理论研究,也随之被重视起来。所谓估计的渐近性,是指估计量随着样本长度不断增加时所具有的各种收敛性。很多文章(如[4—7])研究了滑动平均与自回归等模型参数估计的渐近性质。在这些文章中讨论了参数估计的依概率收     

固定效应模型参数估计方法选择的探究

针对固定效应模型的参数估计问题,目前主要有三种估计方法:组内变换法、差分法、虚拟变量法.通过理论分析与蒙特卡洛模拟实验相结合的方法,在模型误差项存在三种自相关情况下,探究了固定效应模型参数估计方法的选择问题.研究发现:①组内变换法与虚拟变量法完全一致;②当模型误差项不存在自相关时,适合选择组内变换法;③当模型误差项服从...     

分数扩散模型的参数估计及其应用

研究分数扩散模型的参数估计及其应用问题.分数扩散模型是一类由分数Brownian运动驱动的随机微分方程.主要结果有:(1)利用二次变差方法给出模型中扩散系数的估计量,通过最小二乘法给出模型中漂移系数的估计量;(2)证明这些估计量的一致收敛性和渐近正态性;(3)利用MCMC方法对此估计量进行验证,并通过R软件将上述模型以及参数估计量应用到SHIBOR利率中进行实证研究.     

基于两步法带宽选择的金融时间序列长记忆参数估计

金融时间序列长记忆参数的半参数估计方法以频域分析为主,带宽选择是其中必不可少的关键环节。不同的带宽可能给出差异明显的长记忆参数估计值,甚至产生矛盾的结论,进而影响时间序列平稳性的判断。本文提出一种两步法,用于金融时间序列长记忆估计的半参数方法的带宽选择,并进一步对长记忆参数进行估计:首先,为了克服半参数方法忽略短期结构的不足,通过信息准则判断ARFIMA(p,d,q)过程的短记忆结构;其次,用短记忆模型拟合差分后的序列,根据拟合效果确定选择带宽及长记忆参数估计值。数值模拟显示以长记忆参数估计值均方根误差最小为标准,两步法优于其他方法。经上证50指数已实现波动率日数据的实证检验,两步法在长记忆模型中的预测误差最小;与短记忆模型相比,两步法在中期提前预测步长上具有优势。     

最小二乘法的统计学原理及在农业试验分析中的应用

在现实世界中,普遍地存在着变量之间相互联系、相互制约的关系.那么,怎样用一个简单的解析式较为准确地描述和反映变量之间的关系呢?回归分析是最好的数学工具.在回归分析中,估计回归方程经常用到普通最小二乘法.然而,最小二乘法因其抽象常常被大家所忽视,它是从误差拟合角度对回归模型进行参数估计,并在参数估计以及预测、预报等众多农业领域中得到广泛的应用.就最小二乘法的引入,原理的证明,简单的应用进行归纳和总结.探讨了最小二乘法的线性拟合,对非线性拟合作了简要的叙述,使人们对最小二乘法有更为清晰、系统、全面地认识.农业科学研究影响因素多,能产生多种现象,似乎无规律可循,但是,在一定的条件、范围内,是有一定规律可循的,在这里,采用逆向思维的方法,应用普通最小二乘法就能很好地解决这一类问题,它为农业科研分析提供了一种强有力的手段.     

确定Lotka-Volterra生态系统模型高精度参数的研究

研究确定Lotka-Volterra生态系统模型的高精度参数估计问题.利用周期性,先对测量数据进行预处理;然后用三种不同的方法构造了误差函数,进行非线性最小二乘法参数估计;再用计算机仿真对其进行验证.结果表明该方法能够有效地解决高精度参数估计中消除测量数据误差的问题.     

二次型在经济管理中的应用简介

本文是二次型及其定性理论在经济管理中的一些应用的归纳总结,包括多元函数极值存在的充分条件、线性回归模型中参数估计的最小二乘法、随机向量及其线性函数的数字特征、线性组合预测模型的误差平方和以及线性组合投资收益率的方差（风险）等。     

利用数据分组优化度量误差模型的参数估计

在一般的线性回归模型中,自变量都被认为是没有误差的准确值。然而当所有观测变量都可能存在误差时,通常的统计方法就会产生偏差。本文利用数据分组的思想,提出分组最小二乘估计法进行参数估计,减少了参数估计的偏差。并且在只知道误差界的情况下,利用分组最小二乘能给出几种度量误差模型的相合估计。     

基于异方差的自回归预测模型的参数估计及其应用

从齐性方差的线性回归模型参数估计的最小二乘法出发,通过对统计资料的适当变换,利用加权最小二乘法,获得了异方差的线性自回归模型和四种异方差的非线性自回归模型的参数估计公式,并举例阐述了估计公式的应用.     

非随机缺失机制下基于模型的参数似然估计方法研究

在纵向抽样调查活动中,常出现变量数据缺失的情况,如何对含缺失的数据集进行总体参数估计是一个热点话题。目前已有方法主要适用于随机缺失机制下的缺失数据分析问题,常采用插补法生成完整数据集,基于此进行参数估计。本文在非随机数据缺失机制下,研究了几种基于模型的参数似然估计方法,包括模式混合模型法和选择模型法,对单调缺失模式下含缺失纵向调查数据给出了参数估计范例,进而引入随机效应参数,将两种方法加以推广。     

Incorporating minimum Frobenius norm models in direct search

The goal of this paper is to show that the use of minimum Frobenius norm quadratic models can improve the performance of direct-search methods. The approach taken here is to maintain the structure of directional direct-search methods, organized around a search and a poll step, and to use the set of previously evaluated points generated during a direct-search run to build the models. The minimization of the models within a trust region provides an enhanced search step. Our numerical results show that such a procedure can lead to a significant improvement of direct search for smooth, piecewise smooth, and noisy problems.     

广义线性模型在汽车保险定价的应用

对非寿险产品分类费率的厘定通常采用单项分析法、最小偏差法和多元线性回归等方法。虽然这些方法在非寿险产品定价中仍然占有一度之地,但由于保险数据的特殊性,它们的缺陷越来越受到人们的重视。本文简要分析了这些传统定价方法存在的缺陷,介绍了非寿险精算中典型的广义线性模型,并通过汽车第三者责任保险的损失数据说明了广义线性模型在非寿险产品定价中的具体应用,以及应用广义线性模型时应该注意的几个问题。     

Optimizing VVT strategies: a decomposition approach

Verification, validation and testing (VVT) of large systems is an important but complex process. The decisions involved have to consider on one hand the controllable variables associated with investments in appraisal and prevention activities and on the other hand the outcomes of these decisions that are associated with risk impacts and systems' failures. Typically, quantitative models of such large systems use simulation to generate distributions of possible costs and risk outcomes. Here, by assuming independence of risk impacts, we decompose the decision process into separate decisions for each VVT activity and supercede the simulation technique by simple analytical models. We explore various optimization objectives of VVT strategies such as minimum total expected cost, minimum uncertainty as well as a generalized optimization objective expressing Taguchi's expected loss function and provide explicit solutions. A numerical example based on simplified data of a case study is used to demonstrate the proposed VVT optimization procedure.     

Genetic algorithms for portfolio selection problems with minimum transaction lots

Conventionally, portfolio selection problems are solved with quadratic or linear programming models. However, the solutions obtained by these methods are in real numbers and difficult to implement because each asset usually has its minimum transaction lot. Methods considering minimum transaction lots were developed based on some linear portfolio optimization models. However, no study has ever investigated the minimum transaction lot problem in portfolio optimization based on Markowitz’ model, which is probably the most well-known and widely used. Based on Markowitz’ model, this study presents three possible models for portfolio selection problems with minimum transaction lots, and devises corresponding genetic algorithms to obtain the solutions. The results of the empirical study show that the portfolios obtained using the proposed algorithms are very close to the efficient frontier, indicating that the proposed method can obtain near optimal and also practically feasible solutions to the portfolio selection problem in an acceptable short time. One model that is based on a fuzzy multi-objective decision-making approach is highly recommended because of its adaptability and simplicity.     

带区间数据的最小风险斯坦纳树问题

考虑了在带区间数据的不确定网络中, 最小风险和模型以及最小最大风险模型下的斯坦纳树问题. 它们推广了相应模型下的最短路问题和最小支撑树问题, 在网络设计中具有更加广泛的应用.我们分别给出了这两个模型下斯坦纳树问题的近似算法, 并对算法性能做了理论分析和证明. 结果显示我们的算法具有优良的常数逼近的性质, 能在多项式时间内算出令人满意的解.     

非寿险分类费率模型的比较研究和实证分析

非寿险分类费率的厘定通常采用的方法有单项分析法、最小偏差法和广义线性模型,特别是后面两种方法在非寿险实务中应用十分广泛,精算文献中对这两种方法的理论和应用研究也较多,但对二者的比较研究较少。本文首先对最小偏差模型和广义线性模型进行了简要介绍,之后对这两种分类费率模型进行了系统的比较研究,总结了它们各自的优缺点以及二者之间的一些等价关系,最后通过一组实际的汽车保险数据讨论了它们的应用。     

Variable annuities: A unifying valuation approach

Life annuities and pension products usually involve a number of guarantees, such as minimum accumulation rates, minimum annual payments or a minimum total payout. Packaging different types of guarantees is the feature of so-called variable annuities. Basically, these products are unit-linked investment policies providing a post-retirement income. The guarantees, commonly referred to as GMxBs (namely, Guaranteed Minimum Benefits of type ‘x’), include minimum benefits both in the case of death and survival. In this paper we propose a unifying framework for the valuation of variable annuities under quite general model assumptions. We compute and compare contract values and fair fee rates under ‘static’ and ‘mixed’ valuation approaches, via ordinary and least squares Monte Carlo methods, respectively.     

动态自融资与消费策略的多目标控制模型

在不考虑交易费用的前提下,本文研究了投资者最优动态自融资与消费策略,建立了两种多目标控制模型,分别考虑了使投资者的累积消费效用与／或拥有的财富的效用较大风险较小两个目标。对传统的侧重于单纯追求消费或财富效用达到极大的方法进行了改进,给出了相关分析结果。     

Rationality,minimality and uniqueness of representation of matrix formal power series

In some multivariate time-series models a matrix power series is involved. These models can be identified as rational models if these series correspond to a matrix rational function. Moreover, it is necessary to answer some questions about minimality and uniqueness of representation. The main results of this paper fall within the sphere of matrix Padé approximation. On the basis of formal power series, matrix rational functions of arbitrary dimensions are characterized. Furthermore, we study certain minimality types, that are, global minimum degrees and row minimum degrees. In addition, given that the rational representation of the function for the same pair of degrees need not be unique, we have obtained conditions to study the uniqueness of said representation and, also, to find a “canonical” unique representation. Moreover, we consider an application to special series which is associated with time-series models; such series leads to new theoretical results relating to matrix Padé approximation. Finally, we comment on some illustrative examples.     

Implementation of high‐order variational models made easy for image processing

High‐order variational models are powerful methods for image processing and analysis, but they can lead to complicated high‐order nonlinear partial differential equations that are difficult to discretise to solve computationally. In this paper, we present some representative high‐order variational models and provide detailed descretisation of these models and numerical implementation of the split Bregman algorithm for solving these models using the fast Fourier transform. We demonstrate the advantages and disadvantages of these high‐order models in the context of image denoising through extensive experiments. The methods and techniques can also be used for other applications, such as image decomposition, inpainting and segmentation. Copyright © 2016 John Wiley & Sons, Ltd.