混合系数线性模型的几乎无偏岭估计

本文研究了连续测量数据情况下的混合系数线性模型的参数估计问题.利用岭估计方法得到了该模型的几乎无偏岭估计,并证明了在均方误差意义下,几乎无偏岭估计优于岭估计.最后讨论了有偏参数的选取问题.     

测量误差数据下线性模型的几乎无偏岭估计

文章讨论带测量误差的线性模型中参数估计的问题.当带测量误差的线性模型存在复共线的时候,通过几乎无偏估计的思想,提出了几乎无偏岭估计,并对估计的性质进行分析.通过研究发现几乎无偏岭估计不但能克服复共线性,同时有比较小的均方误差.     

混合系数线性模型的几乎无偏s-K估计

在连续测量数据情况下,给出了混合系数线性模型的几乎无偏s-K估计,讨论了该估计的相关性质,并在一定条件下证明了几乎无偏s-K估计优于s-K估计以及几乎无偏岭估计.     

半参数回归模型的一类压缩估计

研究了半参数回归模型的参数估计问题,利用压缩估计方法给出了模型的一类有偏估计,并与最小二乘估计、岭估计、几乎无偏岭估计进行了比较.在均方误差意义下,新的压缩估计明显优于最小二乘估计.最后讨论了有偏参数选取的问题.     

聚集数据多元线性模型参数的多元聚集广义岭估计的相对效率

对于聚集数据的多元线性模型,提出了参数的多元聚集广义岭估计的概念,给出了多元聚集广义岭估计相对于最小二乘估计及最佳线性无偏估计的两种相对效率,并得到了这两种相对效率的上界.     

多元线性模型回归系数的有偏估计与均方误差的无偏估计

本文对多元线性模型回归系数的最小二乘估计的任一线性变换，给出了均方误差的一个无偏估计，并应用统一方法，即极小化均方误差的无偏估计的方法，对岭估计和广义岭估计给出了确定偏参数的公式。最后给出了一个实例。     

聚集数据多元线性模型参数的多元聚集综合岭估计的相对效率

对于聚集数据的多元线性模型,提出了参数的多元聚集综合岭估计的概念,给出了多元聚集综合岭估计相对于最小二乘估计及最佳线性无偏估计的两种相对效率,并得到了这两种相对效率的上界.应用Monte Carlo模拟,验证了有关结论是合理的.     

生长曲线模型中基于奇异值分解的岭估计

在生长曲线模型中将设计阵的奇异值分解与普通的岭估计相结合,针对设计阵A与C至少有一个病态时的情况提出生长曲线模型中基于奇异值分解的岭估计.比较其在均方误差,均方误差矩阵,及PC准则下相对于最小二乘估计的优良性.证明其容许性并利用Hemmerle和Brantle用于确定广义岭估计参数的方法给出极小化均方误差的无偏估计法选取岭参数.     

多元线性模型中两类预测的最优性判别

在一般多元线性模型中就基于岭估计的预测量与最优线性无偏预测量的最优性判别问题进行了讨论,得到了基于岭估计的预测量在矩阵迹意义下优于最优线性无偏预测量的充要条件.     

增长曲线模型回归系数的广义岭估计

本文采用广义岭估计β（Ｋ）来估计增长曲线模型中回归系数β＝ｖｅｃ（Ｂ），通过Ｋ值的选取，可使其均方误差（ＭＳＥ）小于ＬＳ估计β的ＭＳＥ。同时对ＬＳ估计的任一线性变换，给出了其均方误差的一个无偏估计，并应用极小化β（Ｋ）的ＭＳＥ的无偏估计的方法，得到了确定岭参数的公式。     

回归系数的广义岭型主相关估计及其优良性

In this paper, we propose a new biased estimator of the regression parameters, the generalized ridge and principal correlation estimator. We present its some properties and prove that it is superior to LSE （least squares estimator）, principal correlation estimator, ridge and principal correlation estimator under MSE （mean squares error） and PMC （Pitman closeness） criterion, respectively.     

广义岭估计优于最小二乘估计的两个充分条件

分别给出了线性回归模型未知参数β的广义岭估计在MSE准则和PC准则下优于LS估计的充分条件.     

基于支持向量回归和核岭回归对血糖值预测的对比分析

为了对比支持向量回归(SVR)和核岭回归(KRR)预测血糖值的效果,本文选择人工智能辅助糖尿病遗传风险的相关数据进行实证分析.首先对数据进行预处理,将处理后的数据导入Python.其次,为了使SVR和KRR的对比结果具有客观性,使用了三种有代表性的核方法(线性核函数,径向基核函数和sigmod核函数).然后,在训练集上采用网格搜索自动调参分别建立SVR和KRR的最优模型,对血糖值进行预测.最后,在测试集上对比分析SVR和KRR预测的均方误差(MSE)和拟合时间等指标.结果表明:均方误差(MSE)都小于0.006,且KRR的MSE比SVR的小0.0002,KRR的预测精度比SVR更高;而SVR的预测时间比KRR的少0.803秒,SVR的预测效率比KRR好.     

对数正态分布场合下恒定应力加速寿命试验的保序估计

讨论了对数正态分布场合下恒定应力和加速寿命试验的最优线性无偏估计及保序估计,获得了保序估计的表达式,并给出了一个数值例子。     

The best EBLUP in the Fay�CHerriot model

We show that in the case of Fay?CHerriot model for small area estimation, there is an estimator of the variance of the random effects so that the resulting EBLUP is the best in the sense that it minimizes the leading term in the asymptotic expansion of the mean squared error (MSE) of the EBLUP. In particular, in the balanced case, i.e., when the sampling variances are equal, this best EBLUP has the minimal MSE in the exact sense. We also propose a modified Prasad?CRao MSE estimator which is second-order unbiased and show that it is less biased than the jackknife MSE estimator in a suitable sense in the balanced case. A real data example is discussed.     

Superiority of empirical Bayes estimator of the mean vector in multivariate normal distribution

In this paper, the Bayes estimator and the parametric empirical Bayes estimator (PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator (MVUE) and a revised James-Stein estimators (RJSE) are investigated respectively under mean square error (MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.     

Threshold optimization for classification in imbalanced data in a problem of gamma-ray astronomy

We introduce a method to minimize the mean square error (MSE) of an estimator which is derived from a classification. The method chooses an optimal discrimination threshold in the outcome of a classification algorithm and deals with the problem of unequal and unknown misclassification costs and class imbalance. The approach is applied to data from the MAGIC experiment in astronomy for choosing an optimal threshold for signal-background-separation. In this application one is interested in estimating the number of signal events in a dataset with very unfavorable signal to background ratio. Minimizing the MSE of the estimation is a rather general approach which can be adapted to various other applications, in which one wants to derive an estimator from a classification. If the classification depends on other or additional parameters than the discrimination threshold, MSE minimization can be used to optimize these parameters as well. We illustrate this by optimizing the parameters of logistic regression, leading to relevant improvements of the current approach used in the MAGIC experiment.     

The Superiorities of Simultaneous Empirical Bayes Estimation for the Regression Coefficients and Error-Variance in Linear Model

When the hyperparameters of prior distribution are partly known in linear model, the simultaneous parametric empirical Bayes estimators (PEBE) of the regression coefficients and error variance are constructed. The superiority of PEBE over the least squares estimator (LSE) of regression coefficients is investigated in terms of the the mean square error matrix (MSEM) criterion, and the superiority of PEBE over LSE of the error variance is discussed under the the mean square error (MSE) criterion. Finally, when all hyperparameters are unknown, the PEBE of regression coefficients and error variance are reconstructed and the superiority of them over LSE under the MSE criterion are studied by simulation methods.     

Traveling wave solutions of the nonlinear Drinfel’d–Sokolov–Wilson equation and modified Benjamin–Bona–Mahony equations

In this paper, the modified simple equation (MSE) method is implemented to find the exact solutions for the nonlinear Drinfel’d–Sokolov–Wilson (DSW) equation and the modified Benjamin–Bona–Mahony (mBBM) equations. The efficiency of this method for constructing these exact solutions has been demonstrated. It is shown that the MSE method is direct, effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this technique reduces the large volume of calculations.