缺失数据下半参数空间自回归模型的估计

本文研究了响应变量随机缺失时部分线性空间自回归模型的估计问题.结合B样条方法,我们给出了该模型参数部分和非数部分的极大似然估计的EM算法、伪限制极大似然估计的EM算法、以及边际极大似然估计算法,并通过数值模拟比较了三种估计和相应算法在不同的样本容量、缺失比例及空间权重矩阵下数值表现.最后,通过一个实际例子进一步验证三种方法的优良性.     

指数函数与幂函数回归计算的极大似然法及其应用

为提高拟合精度,研究了指数函数与幂函数非线性回归计算的极大似然法.分析表明,在指数函数与幂函数回归计算的因变量为正态随机变量的情况下,极大似然估计与非线性回归的最小二乘估计具有相同的结果;导出了极大似然法求解指数函数与幂函数回归参数的方程式,并给出了计算方法.此方法拟合因变量的残差平方和为最小.实例表明,本文方法拟合精度与高斯-牛顿法相当、显著优于线性化的回归方法,而计算方法要比高斯-牛顿法简单方便,易于实现.     

半参数回归模型拟极大似然估计的渐近分布

用拟极大似然估计方法研究了误差为AR(1)时间序列的半参数回归模型,得到了参数及非参数的拟极大似然估计量,并研究了它们的渐近分布.     

基于概率分布对巴音郭楞蒙古自治州风速特征的研究

基于新疆巴音郭楞蒙古自治州风速数据,讨论了分布参数估计方法和分布模型选择准则,发现混合威布尔分布是一个非常灵活的分布.采用极大似然方法和最小二乘方法,并运用四种优化算法找到参数最优估计值.同时,使用8种测度指标多重判断分布的适用性.对于混合威布尔分布,采用最小二乘法估计模型参数时,得到的分布能较好地拟合该地区风速.结果对相关部门实际分析巴音郭楞蒙古自治州风速特征和风能潜力具有参考价值.     

利用样本分位数的Logistic总体分布参数的近似最佳线性无偏估计

Harter H_L.,Balakrishnan N.等先后讨论了Logistic总体分布参数的极大似然估计,近似极大似然估计;其后Ogawa J.,Lloyd E.H.,Kulldorff G.,Gupta S.S,及chan L.K. 等又先后讨论了Logistlic分布参数的最佳线性无偏估计及估计的相对效率等问题.令人遗憾的是:在大样本情形下,上述估计均难以求得.为缓解这一困难,本文讨论利用样本分位数的Logistic总体的近似最佳线性无偏估计,给出估计量的大样本性质,以及样本分位数不超过10情形下,估计量有渐近最大相对估计效率时样本分位数的选取方案等.     

有限混合Laplace分布回归模型局部估计的EM算法

本文研究了一类有限混合Laplace分布回归模型的局部极大似然估计问题. 利用核回归方法和最大化局部加权似然函数的EM算法, 获得了参数函数的局部极大似然估计量, 并讨论了它们的渐近偏差, 渐近方差和渐近正态性. 推广了有限混合回归模型下局部非参数估计的结果.     

有限混合Laplace分布回归模型局部估计的EM算法（英文）

本文研究了一类有限混合Laplace分布回归模型的局部极大似然估计问题.利用核回归方法和最大化局部加权似然函数的EM算法,获得了参数函数的局部极大似然估计量,并讨论了它们的渐近偏差,渐近方差和渐近正态性.推广了有限混合回归模型下局部非参数估计的结果.     

Gumbel分布参数估计及在水位资料分析中应用

本文利用Gumbel分布拟合某条河流三个观测站的历年最高水位资料.我们用分位数法、极大似然法、概率加权矩法对Gumbel分布中的参数进行估计,不仅从理论上而且利用蒙特卡洛方法讨论了三种估计方法的统计性质,并给出了三个观测站处的T年一遇的最高水位数据.我们认为极大似然法给出的估计量在各个方面都有好的且稳定的表现.     

AR(p)模型中的变点分析

本文分别用极大似然法和Bayes方法研究了AR(p)模型中的变点问题.在数据矩阵不一定满秩的条件下,利用Moore-Penrose广义逆给出了模型参数的极大似然估计的统一表达式和变点位置的估计式.在假定自回归系数的先验分布服从多元正态,方差服从逆Γ分布的条件下,用Bayes方法给出了变点位置估计的显示表达式以及模型参数的Bayes估计.     

回归模型的同方差检验

本文利用局部经验似然和WNW方法对条件分布函数和条件分位数进行估计,并利用条件分位数的方法对回归模型中的误差方差进行了同方差假设检验,获得了零假设下检验统计量的渐近分布为X2分布．模拟计算表明同方差假设检验的条件分位数方法具有较好的功效．     

Optimizing logistic regression coefficients for discrimination and calibration using estimation of distribution algorithms

Logistic regression is a simple and efficient supervised learning algorithm for estimating the probability of an outcome or class variable. In spite of its simplicity, logistic regression has shown very good performance in a range of fields. It is widely accepted in a range of fields because its results are easy to interpret. Fitting the logistic regression model usually involves using the principle of maximum likelihood. The Newton–Raphson algorithm is the most common numerical approach for obtaining the coefficients maximizing the likelihood of the data. This work presents a novel approach for fitting the logistic regression model based on estimation of distribution algorithms (EDAs), a tool for evolutionary computation. EDAs are suitable not only for maximizing the likelihood, but also for maximizing the area under the receiver operating characteristic curve (AUC). Thus, we tackle the logistic regression problem from a double perspective: likelihood-based to calibrate the model and AUC-based to discriminate between the different classes. Under these two objectives of calibration and discrimination, the Pareto front can be obtained in our EDA framework. These fronts are compared with those yielded by a multiobjective EDA recently introduced in the literature.      

Functional relationships having many independent variables and errors with multivariate normal distribution

This paper deals with maximum likelihood estimation of linear or nonlinear functional relationships assuming that replicated observations have been made on p variables at n points. The joint distribution of the pn errors is assumed to be multivariate normal. Existing results are extended in two ways: first, from known to unknown error covariance matrix; second, from the two variate to the multivariate case.For the linear relationship it is shown that the maximum likelihood point estimates are those obtained by the method of generalized least squares. The present method, however, has the advantage of supplying estimates of the asymptotic covariances of the structural parameter estimates.     

Empirical likelihood analysis of the Buckley-James estimator

The censored linear regression model, also referred to as the accelerated failure time (AFT) model when the logarithm of the survival time is used as the response variable, is widely seen as an alternative to the popular Cox model when the assumption of proportional hazards is questionable. Buckley and James [Linear regression with censored data, Biometrika 66 (1979) 429-436] extended the least squares estimator to the semiparametric censored linear regression model in which the error distribution is completely unspecified. The Buckley-James estimator performs well in many simulation studies and examples. The direct interpretation of the AFT model is also more attractive than the Cox model, as Cox has pointed out, in practical situations. However, the application of the Buckley-James estimation was limited in practice mainly due to its illusive variance. In this paper, we use the empirical likelihood method to derive a new test and confidence interval based on the Buckley-James estimator of the regression coefficient. A standard chi-square distribution is used to calculate the P-value and the confidence interval. The proposed empirical likelihood method does not involve variance estimation. It also shows much better small sample performance than some existing methods in our simulation studies.     

A Note on Random Effects Growth Curve Models

The robustness of regression coefficient estimator is a hot topic in regression analysis all the while. Since the response observations are not independent, it is extraordinarily difficult to study this problem for random effects growth curve models, especially when the design matrix is non-full of rank. The paper not only gives the necessary and sufficient conditions under which the generalized least square estimate is identical to the the best linear unbiased estimate when error covariance matrix is an arbitrary positive definite matrix, but also obtains a concise condition under which the generalized least square estimate is identical to the maximum likelihood estimate when the design matrix is full or non-full of rank respectively. In addition, by using of the obtained results, we get some corollaries for the the generalized least square estimate be equal to the maximum likelihood estimate under several common error covariance matrix assumptions. Illustrative examples for the case that the design matrix is full or non-full of rank are also given.     

线性模型参数向量的近似贝叶斯估计

用线性贝叶斯方法去同时估计线性模型中回归系数和误差方差,并在不知道先验分布具体形式的情况下,得到了线性贝叶斯估计的表达式.在均方误差矩阵准则下,证明了其优于最小二乘估计和极大似然估计.与利用MCMC算法得到的贝叶斯估计相比,线性贝叶斯估计具有显式表达式并且更方便使用.对于几种不同的先验分布,数值模拟结果表明线性贝叶斯估...     

基于最优估计的数据融合理论

本文提出了一种最优加权的数据融合方法，分析了最优权值的分配原则；给出了多源信息统一的线性融合模型，使其表示不受数据类型和融合系统结构的限制，并指出在噪声协方差阵正定的前提下，线性最小方差估计融合和加权最小二乘估计融合是等价的；介绍了数据融合中的Bayes极大后验估计融合方法，给出了利用极大后验法进行传感器数据融合的一般表示公式；最后以两传感器数据融合为例，证明了利用Bayes极大后验估计进行两传感器数据融合所得到的融合状态的精度比相同条件下极大似然估计得到的精度要高，同时它们均优于任一单传感器局部估计精度。     

Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters

The purpose of this paper is two-fold. First, for the estimation or inference about the parameters of interest in semiparametric models, the commonly used plug-in estimation for infinite-dimensional nuisance parameter creates non-negligible bias, and the least favorable curve or under-smoothing is popularly employed for bias reduction in the literature. To avoid such strong structure assumptions on the models and inconvenience of estimation implementation, for the diverging number of parameters in a varying coefficient partially linear model, we adopt a bias-corrected empirical likelihood (BCEL) in this paper. This method results in the distribution of the empirical likelihood ratio to be asymptotically tractable. It can then be directly applied to construct confidence region for the parameters of interest. Second, different from all existing methods that impose strong conditions to ensure consistency of estimation when diverging the number of the parameters goes to infinity as the sample size goes to infinity, we provide techniques to show that, other than the usual regularity conditions, the consistency holds under moment conditions alone on the covariates and error with a diverging rate being even faster than those in the literature. A simulation study is carried out to assess the performance of the proposed method and to compare it with the profile least squares method. A real dataset is analyzed for illustration.     

Estimating the parameters of a fatigue model using Benders’ decomposition

This paper shows how Benders decomposition can be used for estimating the parameters of a fatigue model. The objective function of such model depends on five parameters of different nature. This makes the parameter estimation problem of the fatigue model suitable for the Benders decomposition, which allows us to use well-behaved and robust parameter estimation methods for the different subproblems. To build the Benders cuts, explicit formulas for the sensitivities (partial derivatives) are obtained. This permits building the classical iterative method, in which upper and lower bounds of the optimal value of the objective function are obtained until convergence. Two alternative objective functions to be optimized are the likelihood and the sum of squares error functions, which relate to the maximum likelihood and the minimum error principles, respectively. The method is illustrated by its application to a real-world problem.     

A note on the simple structural regression model

In this paper we investigate some aspects like estimation and hypothesis testing in the simple structural regression model with measurement errors. Use is made of orthogonal parametrizations obtained in the literature. Emphasis is placed on some properties of the maximum likelihood estimators and also on the distribution of the likelihood ratio statistics.     

Estimating parameters in one-way analysis of covariance model with short-tailed symmetric error distributions

We consider one-way analysis of covariance (ANCOVA) model with a single covariate when the distribution of error terms are short-tailed symmetric. The maximum likelihood (ML) estimators of the parameters are intractable. We, therefore, employ a simple method known as modified maximum likelihood (MML) to derive the estimators of the model parameters. The method is based on linearization of the intractable terms in likelihood equations. Incorporating these linearizations in the maximum likelihood, we get the modified likelihood equations. Then the MML estimators which are the solutions of these modified equations are obtained. Computer simulations were performed to investigate the efficiencies of the proposed estimators. The simulation results show that the proposed estimators are remarkably efficient compared with the conventional least squares (LS) estimators.