方差—协方差矩阵在认知诊断中的作用

认知诊断模型(cognitive diagnostic model,CDM)的统计检验目前主要包括模型参数的标准误估计、项目功能差异检验、项目水平模型比较、Q矩阵修正、属性层级关系探索等5个重要的研究领域。方差—协方差矩阵(信息矩阵的逆矩阵)在CDM的以上5种统计检验中具有基础和核心的作用。文章评述了方差—协方差矩阵在CDM的统计检验中的作用,梳理了以往研究者提出的信息矩阵估计方法的发展思路和脉络。最后对已有研究存在的重要问题进行讨论和展望。

风险价值的方差——协方差计算模型构建及实现

"风险价值(Value At Risk,VaR)"作为一种科学的风险衡量方式,是基于发生损失的概率及损失发生所在的特定时期的一种应用广泛的市场定量工具,是用来评价包括利率风险在内的各种市场风险的方法。由于"风险价值"模型可用来估计因市场风险而发生的资本损失,因此它作为机构投资者有效的风险测量方法有着不可替代的地位。本文就风险价值的方差——协方差计算模型的结构设计、程序代码设计进行了详细阐述并通过具体实例验证了模型的运用和计算机实现。

风险价值VaR及实证研究

随着经济一体化的深入,风险管理受到各个国家和地区越来越多的重视。本文主要讨论了风险管理中的市场风险度量的方法,具体介绍了基于投资组合的收益(或损失)函数的分布函数提出的风险值(VaR)和期望损失(ES)这两种度量方法,它们是目前使用得最广的市场风险度量方法。文中比较了这两种方法的优缺点,给出了各种不同计算VaR和ES的方法,同时也对各种方法进行了对比讨论,给出了一个基于中国上证沪深指数在1999—2013年的日收益率序列的一个实证研究。

基于VaR的汇率风险度量方法文献综述

近年来,随着金融市场全球化、交易系统和通信技术地不断创新,人们对风险度量,如汇率风险度量等的重要性越来越重视。而VaR就是一种基于统计分析基础上的风险度量技术之一,它是对市场汇率风险进行数量化度量的重要工具。在介绍VaR的基本理论方法的基础下,进一步对VaR以及VaR的计算方法进行了较详细的分类介绍,并对各种方法的特点进行讨论和评价。

VAR方法及测定方法简介

本文介绍了VAR风险管理技术以及三种测定方法历史模拟法、方差—协方差分析方法(Var—Cov),蒙特卡拉罗模拟方法(Monte—Carlo)。同时对对VAR方法的特点和应用进行了说明。

VaR理论模型在证券组合投资中实证分析

目前我国的证券投资市场还存在众多不规范的地方,加强金融市场尤其是证券交易市场的风险管理势在必行。目前在国际市场上存在着很多的风险测量的方式,其中VaR模型已成为金融市场上非常重要的测量方式。首先介绍了关于证券组合投资的基本概念及面临的主要风险,再介绍了VaR模型的主要计算方式、优缺点以及VaR模型主要的获取方法。最后重点分析了在VaR约束下使用方差-协方差法的投资组合决策。

A background error covariance model of significant wave height employing Monte Carlo simulation

The quality of background error statistics is one of the key components for successful assimilation of observations in a numerical model.The background error covariance(BEC) of ocean waves is generally estimated under an assumption that it is stationary over a period of time and uniform over a domain.However,error statistics are in fact functions of the physical processes governing the meteorological situation and vary with the wave condition.In this paper,we simulated the BEC of the significant wave height(SWH) employing Monte Carlo methods.An interesting result is that the BEC varies consistently with the mean wave direction(MWD).In the model domain,the BEC of the SWH decreases significantly when the MWD changes abruptly.A new BEC model of the SWH based on the correlation between the BEC and MWD was then developed.A case study of regional data assimilation was performed,where the SWH observations of buoy 22001 were used to assess the SWH hindcast.The results show that the new BEC model benefits wave prediction and allows reasonable approximations of anisotropy and inhomogeneous errors.

An adaptive waveform-detection threshold joint optimization method for target tracking

The joint optimization of detection threshold and waveform parameters for target tracking which comes from the idea of cognitive radar is investigated for the modified probabilistic data association(MPDA)filter.The transmitted waveforms and detection threshold are adaptively selected to enhance the tracking performance.The modified Riccati equation is adopted to predict the error covariance which is used as the criterion function,while the optimization problem is solved through the genetic algorithm(GA).The detection probability,false alarm probability and measurement noise covariance are all considered together,which significantly improves the tracking performance of the joint detection and tracking system.Simulation results show that the proposed adaptive waveform-detection threshold joint optimization method outperforms the adaptive threshold method and the fixed parameters method,which will reduce the tracking error.The average reduction of range error between the adaptive joint method and the fixed parameters method is about 0.6 m,while that between the adaptive joint method and the adaptive threshold only method is about 0.3 m.Similar error reduction occurs for the velocity error and acceleration error.

Unknown parameter’s variance-covariance propagation and calculation in generalized nonlinear least squares problem

The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. The unknown parameter’s vari- ance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source, multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.

Ensemble-based diurnally varying background error covariances and their impact on short-term weather forecasting

Background error covariance(BEC)plays an essential role in variational data assimilation.Most variational data assimilation systems still use static BEC.Actually,the characteristics of BEC vary with season,day,and even hour of the background.National Meteorological Center-based diurnally varying BECs had been proposed,but the diurnal variation characteristics were gained by climatic samples.Ensemble methods can obtain the background error characteristics that suit the samples in the current moment.Therefore,to gain more reasonable diurnally varying BECs,in this study,ensemble-based diurnally varying BECs are generated and the diurnal variation characteristics are discussed.Their impacts are then evaluated by cycling data assimilation and forecasting experiments for a week based on the operational China Meteorological Administration-Beijing system.Clear diurnal variation in the standard deviation of ensemble forecasts and ensemble-based BECs can be identified,consistent with the diurnal variation characteristics of the atmosphere.The results of one-week cycling data assimilation and forecasting show that the application of diurnally varying BECs reduces the RMSEs in the analysis and 6-h forecast.Detailed analysis of a convective rainfall case shows that the distribution of the accumulated precipitation forecast using the diurnally varying BECs is closer to the observation than using the static BEC.Besides,the cycle-averaged precipitation scores in all magnitudes are improved,especially for the heavy precipitation,indicating the potential of using diurnally varying BEC in operational applications.

Altimeter significant wave height data assimilation in the South China Sea using Ensemble Optimal Interpolation

The application of ensemble optimal interpolation in wave data assimilation in the South China Sea is presented. A sampling strategy for a stationary ensemble is first discussed. The stationary ensemble is constructed by sampling from 24-h-interval significant wave height differences of model outputs over a long period,and is validated with altimeter significant wave height data,indicating that the ensemble errors have nearly the same probability distribution function. The background error covariance fields expressed by the ensemble sampled are anisotropic. Updating the static samples by season,the seasonal characteristics of the correlation coefficient distribution are reflected. Hindcast experiments including assimilation and control runs are conducted for the summer of 2010 in the South China Sea. The effect of ensemble optimal interpolation assimilation on wave hindcasts is validated using different satellite altimeter data(Jason-1 and 2 and ENVISAT) and buoy observations. It is found that the ensemble-optimal-interpolation-based wave assimilation scheme for the South China Sea achieves improvements similar to those of the previous optimal-interpolation-based scheme,indicating that the practical application of this computationally cheap ensemble method is feasible.

ROBUST KALMAN FILTERING FOR SYSTEMS UNDER NORM BOUNDED UNCERTAINTIES IN ALL SYSTEM MATRICES AND ERROR COVARIANCE CONSTRAINTS

This paper concerns robust Kalman filtering for systems under norm bounded uncertainties in all the system matrices and error covariance constraints. Sufficient conditions are given for the existence of such filters in terms of Riccati equations. The solutions to the conditions can be used to design the filters. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed design procedure.

IMPROVED ANOVAE OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this paper, the problem of estimating the covariance matrix in general linear mixed models is considered. A new class of estimators is proposed. It is shown that this new estimator dominates the analysis of variance estimate under two squared loss functions. Finally, some simulation results to compare the performance of the proposed estimator with that of the analysis of variance estimate are reported. The simulation results indicate that this new estimator provides a substantial improvement in risk under most situations.

Optimal signal design strategy with improper Gaussian signaling in the Z-interference channel

We propose a thoroughly optimal signal design strategy to achieve the Pareto boundary （boundary of the achievable rate region） with improper Gaussian signaling （IGS） on the Z-interference channel （Z-IC） under the assumption that the interference is treated as additive Gaussian noise. Specifically, we show that the Pareto boundary has two different schemes determined by the two paths manifesting the characteristic of improperly transmitted signals. In each scheme, we derive several concise closed-form expressions to calculate each user＇s optimally transmitted power, covariance, and pseudo-covariance of improperly transmitted signals. The effectiveness of the proposed optimal signal design strategy is supported by simulations, and the results clearly show the superiority of IGS. The proposed optimal signal design strategy also provides a simple way to achieve the required rate region, with which we also derive a closed-form solution to quickly find the circularity coefficient that maximizes the sum rate. Finally, we provide an in-depth discussion of the structure of the Pareto boundary, characterized by the channel coefficient, the degree of impropriety measured by the covariance, and the pseudo-covaxiance of signals transmitted by two users.

Some conditional results for conditionally strong mixing sequences of random variables

The relation between strong mixing and conditionally strong mixing is answered by examples,that is,the strong mixing property of random variables does not imply the conditionally strong mixing property,and the opposite implication is also not true.Some equivalent definitions and basic properties of conditional strong mixing random variables are derived,and several conditional covariance inequalities are obtained.By means of these properties and conditional covariance inequalities,a conditional central limit theorem stated in terms of conditional characteristic functions is established,which is a conditional version of the earlier result under non-conditional case.