Estimation of a subset of regression coefficients of interest in a model with non-spherical disturbances

This paper considers the estimation of a subset of regression coefficients in a linear regression model with non-spherical disturbances, when other regression coefficients are of no interest. A family of estimators is considered and its asymptotic distribution is derived. This proposed family of improved estimators is compared with the usual unrestricted FGLS estimator, and dominance conditions are obtained with respect to risk under quadratic loss as well as the Pitman nearness criterion. The results of a numerical simulation are presented to illustrate the risk performance of various estimators.     

威布尔部件的经验贝叶斯评估

在逐步增加Ⅱ型截尾寿命试验下, 讨论了威布尔部件可靠性指标的估计及性质. 基于Linex损失函数, 给出了威布尔部件寿命分布参数、可靠度函数及失效率函数的一致最小方差无偏估计、贝叶斯估计及经验贝叶斯估计, 并证明了经验贝叶斯估计的渐进最优性. 最后运用Monte-Carlo方法对各种估计 的均方误差进行了模拟比较. 结果表明, 经验贝叶斯估计精度高.     

Local Polynomial-Brunk Estimation in Semi-Parametric Monotone Errors-in-Variables Model with Right-Censored Data

This paper introduces a semi-parametric model with right-censored data and a monotone constraint on the nonparametric part.The authors study the local linear estimators of the parametric coefficients and apply B-spline method to approximate the nonparametric part based on grouped data.The authors obtain the rates of convergence for parametric and nonparametric estimators.Moreover,the authors also prove that the nonparametric estimator is consistent at the boundary.At last,the authors investigate the finite sample performance of the estimation.     

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.     

The Asymptotic Properties of Scad Penalized Generalized Linear Models with Adaptive Designs

This paper discusses the asymptotic properties of the SCAD (smoothing clipped absolute deviation) penalized quasi-likelihood estimator for generalized linear models with adaptive designs, which extend the related results for independent observations to dependent observations. Under certain conditions, the authors proved that the SCAD penalized method correctly selects covariates with non-zero coefficients with probability converging to one, and the penalized quasi-likelihood estimators of non-zero coefficients have the same asymptotic distribution they would have if the zero coefficients were known in advance. That is, the SCAD estimator has consistency and oracle properties. At last, the results are illustrated by some simulations.

     

DIAGNOSTICS FOR NONLINEAR REGRESSION MODEL WITH WEIGHTING OR TRANSFORMATION

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New Moment Estimators of the Effective Spread Based on Daily High and Low Prices

This paper proposes five new simple moment estimators of the effective spread based on the covariance estimator of Roll(1984) and the High-Low estimator recently developed by Corwin and Schultz(2012). And then the authors theoretically investigate the statistical properties of six simple High-Low spread estimators including Corwin and Schultz's estimator. The biases and mean squared errors(MSE) of these six estimators have been derived and compared with each other asymptotically,which, together with the subsequent simulation study, reveal explicitly the superior performance of newly developed High-Low estimators over Corwin and Schultz's estimator in both ideal and nonideal conditions. Moreover, this paper also develops GMM estimators constructed by three or more moment conditions and compares with the six simple High-Low estimators. Finally, several example applications on the U.S. and Chinese financial markets are conducted to demonstrate the superior performance of the new High-Low estimators. The results provide alternative choices for identifying the liquidity proxies that well capture different structure of markets.     

加权已实现极差四次幂变差分析及其应用

针对金融高频数而开发的极差波动估计量因能更精确地度量波动率而备受关注. 根据方差有效性结合数值模拟, 推导出了已实现极差多幂次变差族中最优的波动估计量, 并依据无偏性和方差有效性给出了相应的加权估计量. 同时将这些估计量与已实现GRACH模型相结合, 并对模型进行扩展. 实证表明已实现极差四幂次变差是已实 现极差多幂次变差族中最优的波动估计量, 加权的已实现极差四幂次变差能有效消除日历效应的影响, 扩展的已实现GRACH模型在拟合和预测效果上明显优于传统的EGARCH模型.     

ROBUST NONPARAMETRIC REGRESSION BASED ON L_1-NORM AND B-SPLINES

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异方差非参数回归模型均值与方差变点的小波估计与应用

金融市场中,受突发事件的影响反映资产平均收益的均值函数和反映资产收益波动的方差函数都有可能出现变点. 本文讨论了均值和方差都存在变点的异方差非参数回归模型的变点估计问题. 给出均值函数与方差函数的局部线性估计,利用函数小波系数的特性求得均值与方差变点位置的估计值并给出其收敛速度.在模拟实验中分析变点估计值的样本特性及均值变点估计与方差变点估计的相互影响.最后通过对两组股票数据的均值变点和方差变点进行估计,说明方法的有效性.     

海杂波协方差矩阵估计及其对目标检测性能的影响

在海杂波中检测有用信号,杂波的协方差矩阵需要利用参考数据进行估计,不同的估计方法对信号的检测性能产生不同的影响。首先,给出了几种杂波协方差矩阵估计,即样本协方差矩阵、正则化样本协方差矩阵、最大似然估计和渐进最大似然估计;然后,分析了海杂波数据的非高斯性和非平稳性;最后,利用正则化匹配滤波器作为信号检测器,分析了不同协方差估计对检测性能的影响。分析结果表明,由于实测数据的非平稳性,检测性能均比仿真数据获得的检测性能要差。而将杂波协方差矩阵的最大似然估计应用于检测器,能够获得较好的检测性能。     

贝叶斯估计和尺度空间滤波相结合的滤波方法

提出了一种贝叶斯估计和尺度空间滤波相结合的滤波方法。信号的小波系数表现出很强的非高斯统计特性,其密度函数可以用推广的拉普拉斯先验分布建模。利用贝叶斯估计能够较好地提取出信号的小波系数,再由小波逆变换恢复信号。贝叶斯估计较好地保留了信号的边缘信息,但滤波信号尚不够平滑。尺度空间滤波在保留信号边缘的同时,还有很好的平滑作用。两者相结合有很好的滤波效果。     

ALL ADMISSIBLE LINEAR ESTIMATES OF REGRESSION COEFFICIENTS UNDER MATRIX LOSS

The necessary and sufficient conditions for a linear estimator of a linear estimable functionof regression coefficients in a general fixed effects linear model with the assumptions of normality to beadmissible in the class of all estimators under matrix liss function are given.For a general randomeffects or mixted effects linear model the necessary and sufficient conditions are obtained too.     

QUADRATIC ADMISSIBLE ESTIMATE OF COVARIANCE IN PSEUDO-ELLIPTICAL CONTOURED DISTRIBUTION

This article mainly discusses the admissibility of quadratic estimate of covariance in pseudo-elliptical distribution.Under the quadratic loss function,the necessary and sufficient conditions thata quadratic estimator is an admissible estimator of covariance in the class of quadratic estimators areobtained.A complete class of the quadratic estimator class is also given.     

Optimal Credibility Estimation of Random Parameters in Hierarchical Random Effect Linear Model

In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases.This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.     

归并数据回归模型的半参数估计方法

基于受限因变量的生存函数,构造归并数据回归模型的一个新的半参数估计量, 并设计多项实验与HP估计量进行模拟比较. 模拟显示, 所构造的估计量具有较好的小样本表现.     

高频数据下高维协方差阵的RCM算法估计与应用

基于因子模型的估计方法是高频数据下高维协方差矩阵估计的一个重要方向.为了解决行业分类门限法的主观性问题,本文使用RCM算法对剔除了主要成分的残差矩阵进行重新排序并进行分块对角化门限处理.本文首先在数值模拟中设定残差矩阵包含分块对角结构并将其顺序打乱,随后使用RCM算法进行重新排序,结果表明其能够还原乱序残差矩阵中所包含的分块对角结构.基于2015年股灾期间和2018全年的高频数据,本文将预平均法和使用RCM进行分块对角处理的POET方法进行结合,并在实证研究中对包括该估计量在内的多种协方差估计量进行了样本外预测效果的比较.结果显示改进后的估计量具有更好的预测能力,进行含总敞口约束的最小方差组合投资时的日内波动率整体较低.     

线性回归模型的非线性稳健估计——基于经验过程理论的研究

线性回归模型参数估计的有效性及对厚尾扰动和离群值的稳健性有进一步改进的余地.本文基于条件分布函数提出线性参数模型的一种新的非线性稳健估计量,利用经验过程理论证明了其相合性和渐近正态性.相对于OLS(ordinary least squares)估计量和常用的稳健LAD(least absolute deviations)和Huber估计量,此估计量可全面把握因变量的分布信息,较准确地由样本数据反映真正的数据生成过程,关于扰动项的厚尾分布具有更好的稳健性,且可更好地消弱极端离群值样本对参数估计的不良影响.多种实验设计的模拟表明,此估计量在有限样本下表现良好;在厚尾扰动或离群值出现的时候,显示出良好的稳健性,且优于OLS、LAD以及Huber估计量的小样本表现.     

自回归模型的加权复合Expectile回归估计及其应用

本文基于充分利用多个Expectile信息能提高参数估计效率的假设,提出了AR模型的加权复合Expectile回归(WCER)估计,探讨了该估计的最优权重,建立了其大样本性质,发现根据由数据驱动的最优权重所获得的WCER估计与最优权重已知时所获得的WCER估计具有相同的渐近有效性.数值模拟表明,当误差为厚尾或非对称分布,所提出的WCER估计大大优于传统最小二乘估计.即使误差分布未知,依然可以得到像极大似然估计一样具有优良统计性质的WCER估计.应用所提出的方法分析恒生指数和标准普尔500指数,实证分析表明:所提出的WCER估计在有效性意义下非常具有竞争力.     

Smooth estimation of ROC curve in the presence of auxiliary information

Receiver operating characteristic (ROC) curve is often used to study and compare two-sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of ROC curve if the auxiliary population information is taken into account. The authors show that the empirical likelihood method can be naturally adapted to make efficient use of the auxiliary information to such problems. The authors propose a smoothed empirical likelihood estimator for ROC curve with some auxiliary information in medical studies. The proposed estimates are more efficient than those ROC estimators without any auxiliary information, in the sense of comparing asymptotic variances and mean squared error (MSE). Some asymptotic properties for the empirical likelihood estimation of ROC curve are established. A simulation study is presented to demonstrate the performance of the proposed estimators.