ASP-Based Programs of Best Linear Unbiased Prediction-Estimated Breeding Values in Breeding Stock

In order to improve the breeding effect of livestock, the data were read from an Excel file with Active Server Page （ASP） programs, and the breeding values of breeding stock were calculated by best linear unbiased prediction （BLUP） method.

Best Linear Unbiased Estimators of Location and Scale Ranked Set Parameters under Moving Extremes Sampling Design

In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling(MERSS).Explicit mathematical expressions of these estimators and their variances are derived.Their relative efficiencies with respect to the minimum variance unbiased estimators(MVUEs)under simple random sampling(SRS)are compared for the cases of some usual distributions.The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.

THE SUPERIORITIES OF BAYES LINEAR UNBIASED ESTIMATION IN PARTITIONED LINEAR MODEL

In this article, the Bayes linear unbiased estimation （BALUE） of parameters is derived for the partitioned linear model. The superiorities of the BALUE over ordinary least square estimator （LSE） are studied in terms of the Bayes mean square error matrix （BMSEM） criterion and Pitman closeness （PC） criterion.

De-correlated unbiased sequential filtering based on best unbiased linear estimation for target tracking in Doppler radar

In target tracking applications,the Doppler measurement contains information of the target range rate,which has the potential capability to improve the tracking performance.However,the nonlinear degree between the measurement and the target state increases with the introduction of the Doppler measurement.Therefore,target tracking in the Doppler radar is a nonlinear filtering problem.In order to handle this problem,the Kalman filter form of best linear unbiased estimation(BLUE)with position measurements is proposed,which is combined with the sequential filtering algorithm to handle the Doppler measurement further,where the statistic characteristic of the converted measurement error is calculated based on the predicted information in the sequential filter.Moreover,the algorithm is extended to the maneuvering target tracking case,where the interacting multiple model(IMM)algorithm is used as the basic framework and the model probabilities are updated according to the BLUE position filter and the sequential filter,and the final estimation is a weighted sum of the outputs from the sequential filters and the model probabilities.Simulation results show that compared with existing approaches,the proposed algorithm can realize target tracking with preferable tracking precision and the extended method can achieve effective maneuvering target tracking.

The Superiorities of Bayes Linear Unbiased Estimator in Multivariate Linear Models

In this article, the Bayes linear unbiased estimator （BALUE） of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator （LSE） is studied in terms of the mean square error matrix （MSEM） criterion and Bayesian Pitman closeness （PC） criterion.

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.

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.

On Concomitants of Record Values from Generalized Farlie-Gumbel-Morgenstem Distribution

In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitants for the general case. The results are then applied to the ease of the two-parameter exponential marginal distributions. Using concomitants of record values we derive the best linear unbiased estimators of parameters of the marginal distributions. Moreover, two methods for obtaining predictors of concomitants of record values are presented. Finally, a numerical illustration is performed to highlight the theoretical results obtained.

线性GMDH参数模型的无偏估计研究

多元线性回归分析中,参数无偏性是参数估计方法的一个重要指标。本文对线性GMDH参数模型建立多元线性模型进行了研究,得到以下结论:一、在满足经典线性回归模型的假设条件下,其参数估计量具有无偏的性质;二、在满足其他假设条件下,可以在样本量少于待估参数的情况下建模,估计的参数也是无偏的;三、用参数GMDH方法建模时,它对完全多重共线性是免疫的。

One compound approach combining factor-analytic model with AMMI and GGE biplot to improve multi-environment trials analysis

To improve multi-environmental trial(MET)analysis,a compound method—which combines factor analytic(FA)model with additive main effect and multiplicative interaction(AMMI)and genotype main effect plus genotype-by-environment interaction(GGE)biplot—was conducted in this study.The diameter at breast height of 36 open-pollinated(OP)families of Pinus taeda at six sites in South China was used as a raw dataset.The best linear unbiased prediction(BLUP)data of all individual trees in each site was obtained by fitting the spatial effects with the FA method from raw data.The raw data and BLUP data were analyzed and compared by using the AMMI and GGE biplot.BLUP results showed that the six sites were heterogeneous and spatial variation could be effectively fitted by spatial analysis with the FA method.AMMI analysis identified that two datasets had highly significant effects on the site,family,and their interactions,while BLUP data had a smaller residual error,but higher variation explaining ability and more credible stability than raw data.GGE biplot results revealed that raw data and BLUP data had different results in mega-environment delineation,test-environment evaluation,and genotype evaluation.In addition,BLUP data results were more reasonable due to the stronger analytical ability of the first two principal components.Our study suggests that the compound method combing the FA method with the AMMI and GGE biplot could improve the analysis result of MET data in Pinus teada as it was more reliable than direct AMMI and GGE biplot analysis on raw data.

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.

具相关关系的设计年径流计算统计试验研究

采用AR(1)模型生成非独立的年径流序列样本,以参数和设计值的不偏性和有效性为评价标准,通过统计试验分析了自相关系数ρ、离势系数CV0,系列长度n等对设计年径流量的影响。试验结果表明,ρ、CV0越大,n越小,估计的设计值越不稳定,精度越差,即相关性较大时,常用的适线法估计的适用性值得研究。

MOTION COMPENSATION FOR HIGH RESOLUTION AIRBORNE SAR WITH IMU & GPS

Inertial measurement unit (IMU) is a standard motion sensor in modern airborne SAR systems. But how to remove its systematic error is a difficult problem, which impacts the improvement of resolution in azimuth. The technique of motion compensation presented in this paper, uses the GPS as a reference system to estimate and correct the systematic error of the IMU on the concept of linear unbiased minimum variance (LUMV). This new and effective method achieves very accurate position measurement (both high and low frequency) of the APC in not only short but also long terms, so that it can satisfy the requirement of high resolution airborne SAR. In the last section of the paper, some experimental simulations from raw data are given.

Identification of main effect and epistatic QTLs controlling initial flowering date in cultivated peanut(Arachis hypogaea L.)

Initial flowering date(IFD)is closely related to mature period of peanut pods.In present study,a population of recombinant inbred lines(RIL)derived from the cross between Silihong(female parent)and Jinonghei 3(male parent)was used to map QTLs associated with IFD.The RIL population and its two parental cultivars were planted in two locations of Hebei Province,China from 2015 to 2018(eight environments).Based on a high-density genetic linkage map(including 2996 SNP and 330 SSR markers)previously constructed in our laboratory,QTLs were analyzed using phenotypic data and the best linear unbiased prediction(BLUP)value of initial flowering date by inclusive composite interval mapping(ICIM)method.Interaction effects between every two QTLs and between individual QTL and environment were also analyzed.In cultivated peanut,IFD was affected by genotypic factor and environments simultaneously,and its broad sense heritability(h2)was estimated as 86.8%。Using the IFD phenotypic data from the eight environments,a total of 19 QTLs for IFD were detected,and the phenotypic variation explained(PVE)by each QTL ranged from 1.15 to 21.82%.Especially,five of them were also detected by the BLUP value of IFD.In addition,12 additive QTLs and 35 pairs of epistatic QTLs(62 loci involved)were identifed by the joint analysis of IFD across eight environments.Three QTLs(qIFDB04.1,qIFDB07.1 and qIFDB08.1)located on chromosome B04,B07 and B08 were identified as main-effect QTL for IFD,which had the most potential to be used in peanut breeding.This study would be helpful for the early-maturity and adaptability breeding in cultivated peanut.

非线性Resilient函数的构造

研究了非线性Resilient函数的构造问题。分别给出了利用Resilient函数与其分量函数之间的关系构造Resilient函数和由线性纠错码构造非线性Resilient函数,以及通过置换由线性Re silient函数得到非线性Resilient函数的方法。

Genetic Dissection of Grain Size Traits Through Genome-Wide Association Study Based on Genic Markers in Rice

Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance makes these traits complex to breed on account of several alleles contributing to the complete trait expression.We employed genome-wide association study in an association panel of 88 rice genotypes using 142 new candidate gene based SSR(cgSSR)markers,derived from yield-related candidate genes,with the efficient mixed-model association coupled mixed linear model for dissecting complete genetic control of grain size traits.A total of 10 significant associations were identified for four grain size-related characters(grain weight,grain length,grain width,and length-width ratio).Among the identified associations,seven marker trait associations explain more than 10%of the phenotypic variation,indicating major putative QTLs for respective traits.The allelic variations at genes OsBC1L4,SHO1 and OsD2 showed association between 1000-grain weight and grain width,1000-grain weight and grain length,and grain width and length-width ratio,respectively.The cgSSR markers,associated with corresponding traits,can be utilized for direct allelic selection,while other significantly associated cgSSRs may be utilized for allelic accumulation in the breeding programs or grain size improvement.The new cgSSR markers associated with grain size related characters have a significant impact on practical plant breeding to increase the number of causative alleles for these traits through marker aided rice breeding programs.

Fisher information for generalized Rayleigh distribution in ranked set sampling design with application to parameter estimation

In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size.In order to give more insight into the performance of RSS with respect to(w.r.t.)simple random sampling(SRS),a modified unbiased estimator and a modified best linear unbiased estimator(BLUE)of scale and shape λ and α from GR distribution in SRS and RSS are studied.The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.

Family Selection as a Strategy for Stem Borer (Eldana Saccharina Lepidoptera: Pyralidae) Resistance Breeding in South Africa

Eldana saccharina is the most damaging stem borer of sugarcane in South Africa causing US$90 million losses of revenue annually. The breeding strategy at the South African Sugarcane Research Institute is based on evaluating parents for breeding values using progeny data derived from family plots and selecting parents with high breeding values for crossing. Family selection entails selecting whole populations of progenies based on family mean. The objective of this study was to evaluate the contribution of family selection to eldana resistance breeding. Data were collected from stage 1 (seedlings stage) trials. In each plot, stalks were examined for eldana entry and exit holes and stalks with borings were counted. The number of bored stalks was expressed as a percent of total stalks and subjected to analysis of variance. The family broad sense heritabilities ranged from 0.51 - 0.56 compared with 0.17 for Individual Genotype Selection (IGS). Predicted family selection gains ranged from 20% to 69% compared with 18% for IGS indicating the value of family selection. Female parental effects F-values (1.63 - 2.01) were significant (P = 0.0017 - 0.0041) compared with non-significant male F-values (1.33 - 1.41) and (P = 0.088 - 0.1464) suggesting maternal effects. Crossing parents with higher resistance such as 96M0058 × 94M0017, 87M0965 × 98G1166 and 97M0653 × 94M0017 produced significantly (P < 0.05) fewer bored stalks compared with those showing lower resistance (96H0590 × 95H0167, 94F2694 × 86F3326 and 76L1295 × 91L1492) suggesting additive genetic effects and that recurrent selection will be an effective breeding method.

Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method,with consideration for the model uncertainty.The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method.First,the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction risk.Second,the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models.The effectiveness of the proposed method is verified through numerical analyses.

A Study of the Equivalence of the BLUEs between a Partitioned Singular Linear Model and Its Reduced Singular Linear Models

Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X 1 : X 2) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ 1: β′2 )′ with β1 and β2 being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M 2 X 1β1under the model and its best linear unbiased estimators under the reduced linear models of are given, where M 2 = I -X 2 X 2 + . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M 2 X 1β1 under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model.