Generalized Penalized Least Squares and Its Statistical Characteristics

The solution properties of semiparametric model are analyzed, especially that penalized least squares for semiparametric model will be invalid when the matrix B^TPB is ill-posed or singular. According to the principle of ridge estimate for linear parametric model, generalized penalized least squares for semiparametric model are put forward, and some formulae and statistical properties of estimates are derived. Finally according to simulation examples some helpful conclusions are drawn.

A New Algorithm for Generalized Least Squares Factor Analysis with a Majorization Technique

Factor analysis (FA) is a time-honored multivariate analysis procedure for exploring the factors underlying observed variables. In this paper, we propose a new algorithm for the generalized least squares (GLS) estimation in FA. In the algorithm, a majorization step and diagonal steps are alternately iterated until convergence is reached, where Kiers and ten Berge’s (1992) majorization technique is used for the former step, and the latter ones are formulated as minimizing simple quadratic functions of diagonal matrices. This procedure is named a majorizing-diagonal (MD) algorithm. In contrast to the existing gradient approaches, differential calculus is not used and only elmentary matrix computations are required in the MD algorithm. A simuation study shows that the proposed MD algorithm recovers parameters better than the existing algorithms.

THE INEFFICIENCY OF THE LEAST SQUARES ESTIMATOR AND ITS BOUND

It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.

Likelihood and Quadratic Distance Methods for the Generalized Asymmetric Laplace Distribution for Financial Data

Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.

GENERALIZED MULTIVARIATE RIDGE REGRESSION ESTIMATE AND CRITERIA Q(c) FOR CHOOSING MATRIX K

When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridge estimate(K)of the regression coefficient=vec(B)is considered in multivaiale linear regression model.The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses.In order to overcome these weaknesses,a new family of criteria Q(c)is adpoted which includes the criterion MSE and criterion LS as its special case.The good properties of the criteria Q(c)are proved and discussed from theoretical point of view.The statistical meaning of the scale c is explained and the methods of determining c are also given.

基于渐消因子的ECEF-GLS估计算法

传统的误差配准算法假设系统偏差恒定或缓慢变化,当系统误差发生突变或快速变化时,这一假设不再成立。针对这一问题,研究了时变条件下的误差配准算法,引入渐消因子,对常规的基于地心地固坐标系的广义最小二乘算法(generalized least squares algorithm based on the earth-centered earth-fixed coordinate system,ECEF-GLS)进行了修正,弱化历史量测对配准的影响,并对渐消因子的选取问题进行了研究,给出了合理的设计方法。算法验证表明,基于渐消因子的ECEF-GLS估计算法能够对时变的系统偏差进行有效估计,精度满足配准要求。

病态加权最小二乘混合模型的k-Liu估计解法

文章综合加权多源观测模型及最小二乘混合模型,组合两种有偏估计算法得到组合有偏估计算法。利用岭估计与Liu估计形成一种新的有偏估计——k-Liu估计,其可以抵抗法方程系数矩阵的病态性,同时可以有效降低参数估值的均方误差。通过构建目标函数导出k-Liu估计在病态最小二乘混合模型中参数的通用解式、均方误差式和协因数的计算式,推导出k-Liu估计中修正因子的计算式,通过广义交叉检核法确定岭参数。最后,通过多种估计法参与算例解算,得出k-Liu估计可以进一步提升混合最小二乘模型的解算精度。

基于励磁电压方波调制的三级式同步起动/发电机转子初始位置估算方法

现有基于高频注入的三级式同步起动/发电机转子初始位置估算方法由于高频衰减,面临失效风险。该文基于主电机定转子互感,提出一种“基于励磁电压方波调制的三级式同步起动/发电机转子初始位置估算方法”,将励磁电压作为载波,用低频方波对其进行调制后,提取主电机定子侧低频响应电流用于转子初始位置估算。定子逆变器三相下管导通状态下,该方法分为2步:首先对励磁电压进行低频方波调制,采集主电机定子低频感应电流用于转子初始位置预估算;其次,由预估算初始位置,判断励磁电压断电前后相关电流特征,得到包含磁极信息的最终初始位置。所提方法通过虚拟角度变换和方差对采集低频电流进行处理。实验表明所提方法具有较高估算精度。

基于SDW-MMSE的广义特征值稳健波束形成方法

最大输出信噪比(Signal-to-noise ratio,SNR)准则下,广义特征值(Generalized eigenvalue,GEV)波束形成存在复系数难以控制的问题,在复杂的声学环境中容易导致输出信号严重失真。针对复系数估计问题,本文提出一种基于最小均方误差(Minimum mean square error,MMSE)的复系数估计方法,并通过引入语音失真权重因子(Speech distortion weight,SDW),调节降噪效果和语音失真之间的权重关系,进而提出了基于SDW-MMSE的广义特征值稳健波束形成方法。通过最大似然法估计目标信号和噪音信号的功率谱,进而求解主广义特征向量。进一步基于SDW-MMSE估计复系数,将复系数与主广义特征向量相结合,从而得到基于SDW-MMSE的广义特征值稳健波束形成滤波向量。仿真实验结果表明,本文提出的波束形成方法可有效消除相干噪声和非相干噪声,具有输出信噪比高、语音失真少等稳健性能。

Optimal Generalized Biased Estimator in Linear Regression Model

The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed estimator were derived, and the proposed estimator was compared with other existing biased estimators based on sample information in the the Scalar Mean Square Error (SMSE) criterion by using a Monte Carlo simulation study and two numerical illustrations.

Performance of Existing Biased Estimators and the Respective Predictors in a Misspecified Linear Regression Model

In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.

The Relative Efficiency of the Conditional Root Square Estimation of Parameter in Inhomogeneous Equality Restricted Linear Model

This paper made a discuss on the relative efficiency of the generalized conditional root square estimation and the specific conditional root square estimation in paper [1,2] in inhomogeneous equality restricted linear model. It is shown that the generalized conditional root squares estimation has not smaller the relative efficiency than the specific conditional root square estimation, by a constraint condition in root squares parameter, we compare bounds of them, thus, choose appropriate squares parameter, the generalized conditional root square estimation has the good performance on mean squares error.

Estimation of a Linear Model in Terms of Intra-Class Correlations of the Residual Error and the Regressors

Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.

Carrier frequency offset estimation for a generalized OFDMA uplink

A residual carrier frequency offset （CFO） estimation scheme is proposed for the uplink of orthogonal frequency division multiple access （OFDMA） systems. Multiple access interference caused by CFOs in the uplink is investigated, as it severely affects the performance of a classical maximum likelihood （ML） frequency estimator. By the use of the estimated CFOs of the active users, the linear maximum mean square error （LMMSE） equalization is performed before the ML frequency estimator for the interference cancellation, which can help to sufficiently improve the estimation accuracy for the residual CFO of the incoming user. Analysis and simulations show that the modified ML estimator provides a tradeoff between estimation accuracy and computational complexity caused by the LMMSE interference cancellation, and the proposed method allows OFDMA systems flexibly allocating subcarriers to users.

基于测量误差的Fay-Herriot模型在小域估计中的应用研究

Fay-Herriot模型是常用的小域估计模型方法之一。但传统的Fay-Herriot模型未能考虑模型中辅助信息的测量误差问题,这将会影响目标估计量的估计精度。考虑到辅助信息中可能出现测量误差的情形,构建适应性更佳的基于测量误差的Fay-Herriot模型来进行小域估计。首先,利用结构误差模型来关联小域直接估计量和辅助信息,将小域估计模型转化为测量误差模型;其次,采用广义最小二乘法得到小域目标参数的最优线性无偏估计;最后,利用迭代广义最小二乘法来估计模型的未知参数。该模型不仅解决了辅助信息测量误差方差计算困难的问题,同时也提高了小域估计量的稳定性。数值模拟结果显示,与其他Fay-Herriot估计量相比,在辅助信息存在测量误差的小域中,基于测量误差模型的Fay-Herriot估计量均方误差普遍较小,表现也更为稳健。

基于推广的负二项稀疏算子的随机系数INAR(1)模型及其应用

基于推广的负二项稀疏算子构建带有随机系数的一元INAR(1)模型,推导了该模型的概率统计性质,采用最小二乘估计法进行参数估计并进行了数值模拟。最后给出一个实例应用,并将该模型与其他模型进行对比研究,结果显示带有随机系数的基于推广的负二项稀疏算子的一元INAR(1)模型更适用于实际数据。

基于ECEF的广义最小二乘误差配准技术

雷达组网数据处理首先要进行误差配准,来准确地估计和消除系统误差。传统的误差配准技术多基于球极投影,当雷达之间距离较远时,给配准结果引入一定的误差。基于地球中心坐标系(ECEF),提出了一种广义最小二乘的ECEF-GLS误差配准技术,较好地解决了远距离误差配准问题,误差分析表明,如果忽略模型线性化引入的误差,配准结果达到了CRLB下限。最后,使用仿真数据验证了算法的性能,并和Zhou提出的基于ECEF坐标系的最小二乘ECEF-LS误差配准算法进行了比较。

一种基于轨迹灵敏度的发电机参数抗差估计法

提出了一种基于轨迹灵敏度的发电机参数抗差估计方法,可应用于发电机参数在线辨识与仿真模型校正。首先,利用轨迹灵敏度辨识出对电力系统动态过程影响较大的主导参数集作为待估计参数集。然后,基于相量测量单元(PMU)量测数据,采用基于轨迹灵敏度的逐次逼近方法对该模型进行求解,可以快速得到最优估计结果。另外,将一种具有很强抗差能力的最大指数平方估计模型引入到参数估计中,该估计模型具有自动压缩坏数据影响的能力。新英格兰系统的算例表明,所提出的方法有效,且具有很强的抗差能力。

风电场发电机动态等值问题的研究

在研究风电场对电网影响时,为节省仿真时间,常常利用简化的异步电机模型或通过多机等值来简化由多台风电机组组成的风电场模型。笔者提出基于同步发电机传递函数概念的多台异步发电机等值的参数辨识方法,并采用最小二乘法计算等值异步发电机的同步电抗、暂态电抗和转子时间常数。利用MATLAB/SIMULINK工具箱的仿真结果表明了该等值方法的有效性。

含多类型分布式电源的主动配电网分布式三相状态估计

提出一种含多类型分布式电源(DG)的主动配电网分布式三相状态估计方法。首先,建立了DG并网的三相模型,将DG并网分为直接并网和经脉宽调制换流器并网两类。选取交流节点的电压、DG的运行状态为状态变量,采用加权最小二乘求解。对于未配置实时量测的DG,提出了一种添加伪量测的可行方案,以提高网络的可观测性。进一步,为提高主动配电网状态估计的计算效率与数值稳定性,提出一种扩展分区、将外网边界状态量估计值作为本区域伪量测的分布式状态估计方法。最后,实际的算例分析验证了所提方法的有效性。