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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Comparative analysis of recent hydrological models and an attempt to generate new combined products for monitoring terrestrial water storage change

Hydrological models are crucial for characterizing large-scale water quantity variations and correcting GNSS reference station vertical displacements.We evaluated the robustness of multiple models,such as the Global Land Data Assimilation System (GLDAS),the Famine Early Warning System Network Land Data Assimilation System (FLDAS),the National Centers for Environmental Prediction (NCEP),and the WaterGAP Global Hydrology Model (WGHM).Inter-model and outer comparisons with Global Positioning System (GPS) coordinate time series,satellite gravity field Mascon solutions,and Global Precipitation Climatology Centre (GPCC) guide our assessment.Results confirm WGHM's 26% greater effectiveness in correcting nonlinear variations in GPS height time series compared to NCEP.In the Amazon River Basin,a 5-month lag between FLDAS,GLDAS,and satellite gravity results is observed.In eastern Asia and Australia,NCEP's Terrestrial Water Storage Changes (TWSC)-derived surface displacements correlate differently with precipitation compared to other models.Three combined hydrological models (H-VCE,H-EWM,and H-CVM) utilizing Variance Component Estimation (VCE),Entropy Weight Method (EWM),and Coefficient of Variation Method (CVM) are formulated.Correcting nonlinear variations with combined models enhances global GPS height scatter by 15%-17%.Correlation with precipitation increases by 25%-30%,and with satellite gravity,rises from 0.2 to 0.8 at maximum.The combined model eliminates time lag in the Amazon Basin TWSC analysis,exhibiting a four times higher signal-to-noise ratio than single models.H-VCE demonstrates the highest accuracy.In summary,the combined hydrological model minimizes discrepancies among individual models,significantly improving accuracy for monitoring large-scale TWSC.

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.

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.

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.

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.

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.

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。

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。

热带温带玉米群体产量性状遗传力及遗传方差分量的剖析

【目的】评估2个热带群体和7个温带群体的育种价值,并在这些群体之间寻找新的杂种优势模式,为利用这些种质提供有用的科学信息。【方法】采用9个群体的双列杂交设计,得到36个杂交组合;2002～2003年分别在河南省安阳和湖北省十堰进行田间鉴定,获取产量相关性状的试验数据,用混合线性(AD)模型和MINQUE(1)法(minimum norm quadratic unbiased estimation,最小范数二阶无偏估算法)对各性状遗传力、遗传方差分量及其占总表型变异的比率、群体的加性遗传效应和显性遗传效应进行剖析。【结果】联合分析结果显示:各性状的大多数遗传效应值都达到显著(P≤0.05)或极显著水平(P≤0.01)。各遗传方差分量的效应对小区产量贡献大小是显性>显性与环境互作>加性与环境互作>加性;各性状狭义遗传力大小为穗行数>行粒数>穗长>出籽率>百粒重>小区产量,加性效应最好的4个群体是Suwan1(31.69)、Stay green c4(25.44),WBM C4(14.15)和中综4号(10.29);而显性效应比较好的4个组合为3×6(883.65)、1×3(572.20)、1×2(404.2376)和6×7(384.59)。【结论】在温带玉米育种中Suwan1和Stay green c4是最有利用价值的外来种质,它们都与BSSS C9构成杂种优势模式。在育种实践中,可以把Suwan1和Stay green c4杂交重组,并与BSSS C9构成一对温带和热带种质的杂种优势模式,可以进一步进行相互轮回选择。

利用Allan方差分析GPS非差随机模型特性

非差GPS定位中,通常采用以观测值服从高斯白噪声条件的估计准则进行参数求解。研究表明卫星端误差、传播路径误差、测站环境误差等会破坏观测值的白噪声特性,并且未模型化误差同样具有不利影响。这不仅破坏了估计准则的假设条件,而且部分非白噪声有可能被状态参数吸收,影响估计的准确性。本文将观测值白噪声、有色噪声和未模型化误差一同纳入GPS非差随机模型,以验后残差来表征GPS数据的随机特性,进行Allan方差分析,研究噪声成分及其参数。结果表明,GPS非差噪声组合主要为WN+GM,相位白噪声为2.392mm,GM过程噪声为4.450mm/s,相关时间为52.074s,伪距白噪声为0.936m,GM过程噪声为0.833m/s,相关时间为14.737s,相位的GM过程噪声与卫星相关性较大,而其余噪声则与测站相关性较大,大量分析结果表明GPS非差随机模型并不服从高斯白噪声假设,有待精化。

轨道车辆切削式吸能装置吸能特性研究

针对利用金属薄壁结构轴向切削过程吸收能量的吸能装置,采用多元线性回归分析的方法,建立了吸能装置切削吸能过程的界面力稳定值、能量预测模型。采用方差分析的方法对该模型的回归方程和系数进行了显著性检验。研究了刀具前角、切屑圆心角、切削深度和切削速度对切削式吸能过程的影响程度。研究结果表明,预测模型的回归方程是显著的,刀具前角和切屑圆心角对界面力稳定值的影响显著,切削深度和切削速度对界面力稳定值的影响不显著;刀具前角、切屑圆心角和切削深度对吸能的影响显著,切削速度对吸能的影响不显著。