Study on the Prediction of Rice Blast Based on the Unbiased GM (1,1) Model

To create a new prediction model, the unbiased GM （1,1） model is optimized by the five-point slide method in this paper. Then, based on the occurrence areas of dce blast in Enshi District during 1995 -2004, the new model and unbiased GM （1, 1 ） model are applied to predict the occurrence areas of rice blast during 2005 -2010. Predicting outcomes show that the prediction accuracy of five-point unbiased sliding optimized GM （1, 1 ） model is higher than the unbiased GM （1,1） model. Finally, combined with the prediction results, the author provides some suggestion for Enshi District in the prevention and control of rice blast in 2010.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the General Linear Model

Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.

Grey-Markov Model for Road Accidents Forecasting

In order to improve the forecasting precision of road accidents, by introducing Markov chains forecasting method, a grey-Markov model for forecasting road accidents is established based on grey forecasting method. The model combines the advantages of both grey forecasting method and Markov chains forecasting method, overcomes the influence of random fluctuation data on forecasting precision and widens the application scope of the grey forecasting. An application example is conducted to evaluate the grey-Markov model, which shows that the precision of the grey-Markov model is better than that of grey model in forecasting road accidents.

Partial Improvement of Traditional Grey-Markov Model and Its Application on Fault Prediction

Modeling experiences of traditional grey-Markov show that the prediction results are not accurate when analyzed data are rare and fluctuated.So it is necessary to revise or improve the original modeling procedure of the grey-Markov(GM)model.Therefore,a new idea is brought forward that the Markov theory is used twice,where the first time is to extend the original data and the second to calculate and estimate the residual errors.Then by comparing the original data sequence from a fault prediction case with the simulation sequence produced by the use of GM(1,1) and the new GM method,results are conforming to the original data.Finally,an assumption of GM model is put forward as the future work.

线性回归的几乎无偏两参数岭M估计

针对线性回归模型中设计矩阵存在复共线性问题,利用几乎无偏估计和两参数岭估计的思想,提出了几乎无偏两参数岭M估计。在均方误差准则下,得到了几乎无偏两参数岭M估计优于两参数岭M估计、几乎无偏两参数岭估计,并通过数值模拟验证了估计方法和结论的有效性。

EMPIRICAL LIKELIHOOD-BASED INFERENCE IN LINEAR MODELS WITH INTERVAL CENSORED DATA

An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.

Effect of Multipoint Heterogeneity on Nonlinear Transformations for Geological Modeling: Porosity-Permeability Relations Revisited

An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.

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.

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.

基于无偏灰色GM(1,1)的铁精矿品位预测模型

铁精矿品位的准确预测对铁矿选矿厂的生产和管理具有重要意义。为解决选矿厂生产过程中具有随机波动性的铁精矿品位预测问题,提出一种基于线性变换法的无偏灰色GM(1,1)铁精矿品位预测模型。通过采用一种线性变换方法降低铁精矿品位数据序列的波动干扰,将随机波动数据序列转换为单调增长的数据序列,然后将变换后铁精矿品位数据序列代入无偏灰色GM(1,1)模型以实现铁精矿品位预测模型的建模,最后将该预测模型用于两组铁精矿品位数据序列进行了验证。结果表明,基于线性变换的无偏灰色GM(1,1)铁精矿品位预测模型在预测精度和预测性能上优于两个改进的GM(1,1)预测模型,其预测精度均为一级,预测的最小相对误差为0.2%,平均绝对误差均小于1%,模型具有较好的应用性和有效性,为短期预测铁精矿品位提供了一种新途径。

基于动物模型BLUP的杜洛克猪生长及繁殖性状选择进展

【目的】揭示基于动物模型最佳线性无偏预测(animal model best linear unbiased prediction,AM-BLUP)的选择指数对杜洛克猪生长及繁殖性状的选育效果。【方法】在采用AM-BLUP方法估计个体目标性状育种值基础上,以达100 kg体质量日龄(相对权重0.7)和100 kg活体背膘厚(相对权重0.3)为主选性状构建选择指数,对1个闭锁的杜洛克猪群开展持续7年(2013—2019年)的选育,系统分析选育期间猪群6个生长及繁殖性状表型值、估计育种值(estimated breeding value,EBV)、选择指数及近交系数的变化。【结果】相较于2013年,2019年猪群达100 kg体质量日龄、100 kg活体背膘厚和30~100 kg料重比分别极显著缩短4.45 d、降低0.52 mm和降低0.05(P<0.01);初产和经产母猪的总产仔数分别提高0.99头(P<0.05)和1.02头(P>0.05),产活仔数分别提高0.72头和0.49头(P>0.05),21日龄窝重分别降低0.39 kg和提高6.20 kg(P>0.05);主选性状达100 kg体质量日龄和100 kg活体背膘厚的EBV分别极显著降低3.447和0.533(P<0.01),选择指数极显著提高23.62(P<0.01),除30~100 kg料重比外,其余辅选性状的EBV均获得了不同程度改进。选育结束时,群体平均近交系数为3.1973%,年均增量为0.4904%。【结论】基于AM-BLUP的指数选择可有效改良猪的生产性状,但不同性状的具体选择进展会因其遗传特性的不同而异。

可证安全隐写:理论、应用与展望

可证安全隐写追求由来已久,但是由于缺乏可精确采样的载体,导致可证安全隐写的发展沉寂多年,生成模型的快速发展和生成数据的广泛传播给可证安全隐写带来新的技术手段和伪装环境。文章首先从隐写的经验安全与可证安全的区别出发,引出了可证安全隐写的定义;然后介绍了可证安全隐写的理论与经典构造,并给出了生成式人工智能环境下可证安全隐写的现实构造,在总结基于样本索引的可证安全隐写方法的基础上,介绍了基于分布副本索引的新型隐写构造;最后,文章展望了可证安全隐写的发展趋势:包括公钥隐写和协议,以及在性能无损生成数据水印方面的应用。

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance for the General Linear Model

In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.

基于无偏灰色组合动态模型的铁路客运量预测研究

针对目前铁路运输客运量预测在精度方面的不足,提出一种无偏灰色组合动态预测模型,应用于现有铁路客运量的预测。通过借鉴无偏GM(1,1)模型直接建模思想,对传统的灰色Verhulst模型作出改进,即对原始序列作倒数生成,运用新生成的倒数序列建立无偏灰色Verhulst模型,以消除传统的灰色Verhulst模型自身的一些偏差;为进一步提高模型的拟合精度及收敛速度,引入马尔科夫链方法对无偏灰色Verhulst模型的拟合结果进行修正,同时兼顾数据序列具有一定的时效性,构建出无偏灰色组合动态客运量预测模型。以我国兰青铁路某区段2010—2019年共10年的客运量数据作为原始数据,验证模型的可靠性与准确性,并与传统EDGM(1,1)模型、灰色Verhulst模型和无偏灰色Verhulst模型作对比,结果表明,本文模型在预测精度方面更凸显优势,能有效提高预测结果的准确性。

基于修正辅助变量法的船舶操纵响应模型辨识

为了解决有色噪声干扰对船舶操纵响应模型参数的有偏估计问题,本文提出一种递推修正辅助变量最小二乘法对船舶操纵二阶响应模型进行参数辨识。算法在递推辅助变量最小二乘法的基础上,针对辨识模型引入动态滤波模型改善有色噪声的统计特性,使得系统被估参数值在有色噪声干扰的情况下也能无偏趋近于参数真值。为了验证所提算法的有效性,在实船Z形试验数据的基础上,将递推修正辅助变量最小二乘法、递推辅助变量最小二乘法、增广最小二乘法和标准最小二乘法所辨识得到的模型的进行比较。结果表明:递推修正辅助变量最小二乘法的辨识模型相比其余三者的辨识模型与船舶实际航向角的拟合精度和泛化精度更高,对应的均方根拟合误差和均方根泛化误差分别可达到1°和2°以下,最大绝对误差分别在3°和4°以下。

On Bayes linear unbiased estimation of estimable functions for the singular linear model

The unique Bayes linear unbiased estimator (Bayes LUE) of estimable functions is derived for the singular linear model. The superiority of Bayes LUE over ordinary best linear unbiased estimator is investigated under mean square error matrix (MSEM)criterion.

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.

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.

Existence of unbiased estimate of regression parameters in simple linear EV models

It is well known that for one-dimensional normal EV regression model X = x+ u,Y =α+βx+e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and β are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and β under some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and β exist, and the form of the MVUE of a and β are also given.

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.