EMPIRICAL BAYES TEST PROBLEMS OF VARIANCE COMPONENTS IN RANDOM EFFECTS MODEL

Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n-1/2). Finally, an example concerning the main result is given.

Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

UNIVERSAL FORMULAE OF ROBUST ESTIMATES OF PARAMETER VECTOR AND VARIANCE COMPONENTS

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Bootstrap Inference on the Variance Component Functions in the Two-Way Random Effects Model with Interaction

In this paper,using the Bootstrap approach and generalized approach,the authors consider the one-sided hypothesis testing problems for variance component functions in the two-way random effects model.Firstly,the test statistics and confidence intervals for the sum of variance components are constructed.Next,the one-sided hypothesis testing problems for the ratio of variance components are also discussed.The Monte Carlo simulation results indicate that the Bootstrap approach is better than the generalized approach in most cases.Finally,the above approaches are applied to the real data examples of mice blood p H and molded plastic part’s dimensions.

Bootstrap inference of the skew-normal two-way classification random effects model with interaction

In this paper,we consider the statistical inference problems for the fixed effect and variance component functions in the two-way classification random effects model with skewnormal errors.Firstly,the exact test statistic for the fixed effect is constructed.Secondly,using the Bootstrap approach and generalized approach,the one-sided hypothesis testing and interval estimation problems for the single variance component,the sum and ratio of variance components are discussed respectively.Further,the Monte Carlo simulation results indicate that the exact test statistic performs well in the one-sided hypothesis testing problem for the fixed effect.And the Bootstrap approach is better than the generalized approach in the one-sided hypothesis testing problems for variance component functions in most cases.Finally,the above approaches are applied to the real data examples of the consumer price index and value-added index of three industries to verify their rationality and effectiveness.

Simultaneous optimal estimates of fixed effects and variance components in the mixed model

For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained.

A compressed variance component mixed model for detecting QTNs and QTN-by-environment and QTN-by-QTN interactions in genome-wide association studies

Although genome-wide association studies are widely used to mine genes for quantitative traits,the effects to be estimated are confounded,and the methodologies for detecting interactions are imperfect.To address these issues,the mixed model proposed here first estimates the genotypic effects for AA,Aa,and aa,and the genotypic polygenic background replaces additive and dominance polygenic backgrounds.Then,the estimated genotypic effects are partitioned into additive and dominance effects using a one-way analysis of variance model.This strategy was further expanded to cover QTN-by-environment interactions(QEIs)and QTN-by-QTN interactions(QQIs)using the same mixed-model framework.Thus,a three-variance-component mixed model was integrated with our multi-locus random-SNP-effect mixed linear model(mrMLM)method to establish a new methodological framework,3VmrMLM,that detects all types of loci and estimates their effects.In Monte Carlo studies,3VmrMLM correctly detected all types of loci and almost unbiasedly estimated their effects,with high powers and accuracies and a low false positive rate.In re-analyses of 10 traits in 1439 rice hybrids,detection of 269 known genes,45 known gene-by-environment interactions,and 20 known gene-by-gene interactions strongly validated 3VmrMLM.Further analyses of known genes showed more small(67.49%),minor-allele-frequency(35.52%),and pleiotropic(30.54%)genes,with higher repeatability across datasets(54.36%)and more dominance loci.In addition,a heteroscedasticity mixed model in multiple environments and dimension reduction methods in quite a number of environments were developed to detect QEIs,and variable selection under a polygenic background was proposed for QQI detection.This study provides a new approach for revealing the genetic architecture of quantitative traits.

Robust Estimation of Variance Components Model

The classical least-squares methods may only solve LS β when the variance-covariance (matrix ∑(σ2 ∑)) is known (σ2 is unknown and ∑ is known) in linear model. The author thinks that maximum likelihood type estimation (M-estimation) should replace LS estimation. The paper discusses robust estimations of parameter vector and variance components for corresponding error model based on the principle of maximum likelihood type estimations (M-estimations). The influence functions are given respectively.

THE INEFFICIENCY OF LEASTSQUARES IN GAUSS-MARKOV ANDVARIANCE COMPONENT MODELS

The present paper deals with the inefficiency of the least square estimates in linear models.FOr Gauss-Markov model, a new efficiency is proposed and its lower bound is given. FOr variancecomponent model, an efficiency is introduced and its lower bound, which is independent ofunknown parameters, is obtained.

基于方差分量估计的视觉定位方法

针对视觉导航中存在成像特征点的非均匀误差会影响位姿计算准确度的问题,提出一种基于方差-协方差分量估计的视觉定位方法。首先,从理论角度出发分析相机测量过程中随机误差存在形式及影响因素;其次,向双目相机视觉及视觉/惯性融合模型添加随机模型优化模块,构建非线性优化系统;最后,使用KITTI数据集、EuRoC数据集进行测试,对数据进行基于划分的聚类处理,验证得到该方法能够更加有效精准地估计飞行目标的位姿信息,对随机误差具有良好的优化效果。

基于背景差分法的篮球投篮轨迹预测模型构建

为实现动态复杂环境下篮球投篮轨迹的预测,为篮球训练提供指导依据,构建基于背景差分法的篮球投篮轨迹预测模型。该模型基于混合高斯背景差分方法,构建复杂动态环境背景建模,为保证建模效果,引入自适应学习率进行模型优化,并删除背景模型中冗余高斯分量,获取图像中的前景目标图像;基于最大类间方差的阈值分割方法,二值化处理前景目标图像后,采用区域线性增长方法和篮球运动员投篮运动轨迹图形融合模型,提取前景目标图像中的投篮运动特征,实现篮球投篮轨迹预测。实验表明:该模型具有良好的篮球投篮运动图像处理效果,篮球投篮轨迹预测的可决系数指标结果均在0.947以上,预测结果与实际轨迹结果之间吻合程度较好,满足应用需求。

WOMBAT—A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML)

WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http：//agbu. une.edu.au/-kmeyer/wombat.html

THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS

The present paper daisses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model: Y=Xe + e E(e)= 0, Cov(e)=V, an new efficiencyo f least square estimate for linearly estimable function c'r is proposed and its lower bound is giv-en. For variance component model: Y=X + e, E(e)=0, Cov(e)=, an new efficiency of least square estimate for linearly estimable function C'r is introduced for the first timeand its lower bound, which is independent of unknown parameters, is also obtained.

Function-on-Partially Linear Functional Additive Models

We consider a functional partially linear additive model that predicts a functional response by a scalar predictor and functional predictors. The B-spline and eigenbasis least squares estimator for both the parametric and the nonparametric components proposed. In the final of this paper, as a result, we got the variance decomposition of the model and establish the asymptotic convergence rate for estimator.

偏正态混合效应模型中方差分量函数的参数Bootstrap推断

偏正态混合效应模型通过引入偏度参数,以便更好地刻画实际数据偏态特征,所以被广泛应用于众多实际领域.进一步,方差分量的假设检验一直是该模型的热点研究问题.因此,有必要在偏正态分布下系统讨论混合效应模型中方差分量函数的统计推断问题.首先,分别基于参数Bootstrap方法和广义方法探讨单个方差分量、方差分量之和、方差分量之比的单边假设检验和区间估计问题.其次,Monte Carlo结果表明,在所给样本量和参数设置下,参数Bootstrap方法大多数情况下优于广义方法.最后,将上述方法应用于空气质量指数的案例研究中,以验证所给方法的合理性与有效性.

The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

Stochastic models play an important role in achieving high accuracy in positioning,the ideal estimator in the least-squares(LS)can be obtained only by using the suitable stochastic model.This study investigates the role of variance component estimation(VCE)in the LS method for Precise Point Positioning(PPP).This estimation is performed by considering the ionospheric-free(IF)functional model for code and the phase observation of Global Positioning System(GPS).The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes:a)antenna type,b)receiver type,c)the tropospheric effect,and d)the ionosphere effect.The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model.This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions.Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE.The position error difference for the east-west,north-south,and height components was 1.5 cm,4 mm,and 1.8 cm,respectively.Therefore,weight estimation with LS-VCE can provide more appropriate results.Eventually,the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight.According to the results,the LS-VCE has a higher convergence rate than the nominal weight.The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11,13,12,and 9 min,respectively.

Recent Advances in the Geodesy Data Processing

Geodetic functional models,stochastic models,and model parameter estimation theory are fundamental for geodetic data processing.In the past five years,through the unremitting efforts of Chinese scholars in the field of geodetic data processing,according to the application and practice of geodesy,they have made significant contributions in the fields of hypothesis testing theory,un-modeled error,outlier detection,and robust estimation,variance component estimation,complex least squares,and ill-posed problems treatment.Many functional models such as the nonlinear adjustment model,EIV model,and mixed additive and multiplicative random error model are also constructed and improved.Geodetic data inversion is an important part of geodetic data processing,and Chinese scholars have done a lot of work in geodetic data inversion in the past five years,such as seismic slide distribution inversion,intelligent inversion algorithm,multi-source data joint inversion,water reserve change and satellite gravity inversion.This paper introduces the achievements of Chinese scholars in the field of geodetic data processing in the past five years,analyzes the methods used by scholars and the problems solved,and looks forward to the unsolved problems in geodetic data processing and the direction that needs further research in the future.

基于方差的BDS/GPS/GLONASS数据融合及程序实现

基于HELMERT方差分量估计数学模型,实时迭代计算求出最优的权比,提高定位稳定性和精度。并通过上一历元迭代结果作为下一历元计算初值,减少迭代次数。通过实测数据解算表明:相比传统固定权比,该方法使得定位精度在各个方向得到显著提高。特别在观测条件不好的情况下,保证了定位精度和稳定性。

无碴轨道铁路控制网的Helmert方差分量估计

无碴轨道高速铁路施工基桩控制网要求相邻点的相对精度优于1mm,这就要求必须合理地、可靠地、客观地评定测量精度.测量平差中不合理的随机模型影响着平差结果和各项精度指标的合理评定.结合我国刚建成的第一条无碴轨道高速铁路,简要介绍了基桩控制网的建立,探讨了Helmert方差分量估计在基桩控制网数据处理中的应用.结果表明Helmert方差分量估计方法能准确地确定不同类观测值的权比,从而客观、合理、正确地评定各项精度.

电子鼻快速检测区分羊肉中的掺杂鸡肉

为实现掺假羊肉的快速、客观检测,利用电子鼻定性和定量分析混入鸡肉的掺假羊肉糜。单因素试验表明顶空体积、载气流速、样品量和顶空生成时间对电子鼻传感器的响应影响极显著;主成分分析确定了电子鼻检测的较佳条件:样品量10 g、载气流速200 mL/min、顶空容积250 mL及顶空生成时间30 min。在此条件下检测混入鸡肉的掺假羊肉,结果发现采用主成分分析时,掺入鸡肉的比例随主成分一降低而增大,但相邻比例彼此重叠,难以有效区分;采用典则判别分析时,混入不同比例鸡肉的羊肉糜样品能较好地区分;采用主成分回归分析和偏最小二乘回归分析建立的定量预测模型(R2>0.95)能有效预测混入的鸡肉比例。电子鼻在混入鸡肉的掺假羊肉鉴别中具有可行性,论文可为羊肉掺假鉴别提供理论依据。