闭区间[a,b]上随机系数回归模型的最优设计?

随机系数回归模型是一类广泛应用于社会学、经济学、生物学、心理学、药代动力学等科学研究领域的线性模型.本文讨论了闭区间[a, b]上随机系数回归模型基于 D-, G-, A-, Dβ-和 I-最优准则下的几类最优设计问题.证明了在设计准则满足实值单调的条件下最优设计可在设计域端点处获得的结论,并给出了这几类设计准则下最优设计的解析表达式.     

加权非线性随机系数模型异方差性的Score检验

在回归分析中，随机误差的方差齐性的假设往往有助于问题的解决，但方差齐性假设并不总是正确的。在线性和非线性回归中关于异方差的诊断问题已有许多讨论，在韦博成（1995）讨论的加权非线性回归模型的基础上，用随机系数的方法，讨论加权线性随机系统模型中的异方差检验问题，得到了方差齐性检验的Score统计量。     

非线性回归模型相关性和异方差性的检验

本文讨论了误差是一阶自回归序列的非线性回归模型，首先导出了关于误差相关性和异方差性的似然比检验统计量和Ｓｃｏｒｅ检验统计量，随后利用参数正交变换，得到了修正的似然比检验统计量及修正的Ｓｃｏｒｅ检验统计量。此外，当误差项是一阶滑动平均序列时相应的检验问题也作了讨论。     

随机系数泛函自回归模型的遍历性

提出了随机系数泛函自回归模型，得到了几何遍历性的充分条件。     

单指标模型的异方差检验的渐近性质

在回归分析中,通常假定方差齐性。在参数和非参数回归模型中,关于方差齐性的检验问题都有很多的研究。本文利用P-样条方法,研究了单指标模型的异方差问题、一阶自回归问题,给出了异方差问题、一阶自回归问题Score检验统计量的大样本性质。     

异方差混料模型的直积设计及其最优性

混料试验设计在工农业生产、科学试验以及日常生活中具有广泛的应用.传统的混料试验设计大都在试验误差同方差性的假设前提下进行,但是相对而言,试验误差异方差性更符合实际.针对这一问题,本文主要研究了在试验误差异方差性的假设条件下,混料乘积模型直积设计的D-、A-以及线性最优性问题.在给定条件下,通过构建混料齐次子模型的D-、A-或线性最优设计,可以证明其乘积模型的直积设计也是相应的最优设计.     

变系数空间自回归模型的Bootstrap检验

变系数空间自回归模型是变系数模型在空间数据分析方面的推广,因其众多的应用背景而得到广泛的重视和研究,确认模型中系数是否真正随变量的变化而变化是应用变系数空间自回归模型需解决的首要问题.本文基于Bootstrap检验方法研究了变系数空间自回归模型中的常系数项的辨别问题,为建立半变系数空间自回归模型提供依据.最后,通过模拟...     

相依误差下异方差非参数回归模型的样条估计

一些经济金融等实际数据中含有非线性趋势、异方差和相依关系,固定设计和相依误差下的异方差非参数回归模型因其能够反映这些数据特征而有着重要的应用．样条方法是常用的非参数光滑方法之一．为了探究样条方法在这类模型中的可用性,本文在$\alpha$- 混合条件下,讨论了均值函数和方差函数的多项式样条估计的逐点相合性,得到了逐点收敛速度．此外,还对所讨论的方法进行了数值模拟,结果表明样条方法在这类模型的应用中是可行的．     

有约束的混合系数线性模型参数的估计

提供了在连续测量数据的背景情况下，给出了线性模型：{Zi=Xia Yiβi εi i=1,2,……，m βi^i.i.d.～（b,∑）εi^i.i.d.～（0,σ^2Ini)具有约束H（a‘,b‘)‘=0时，固定系数a和随机系数β的一种估计，并讨论了该估计的性质。     

由随机过程的一次实现估计输入数据的方差

目的 为了满足正则化方法求解反问题之需要,提出了一种由随机过程的一次物理实现估计原始数据方差的新方法。方法 通过假设一人上随机误差的分布,然后通过数值仿真得到了方差估算的公式。结果与结论 用不同的随机测量过程对估算方法进行了验证。结果表明,由该方法及公式估算得到的方差具有较高的精度,能比较准确地反映随机误差的内在统计规律。     

Optimal Designs for Random Blocks Model Using Corrected Criteria

Many industrial experiments involve random factors. The random blocks model defines a covariance structure in the data, thus generalized least square estimators of the parameters are used, and their covariance matrix is usually computed using the inverse of the generalized least square estimators information matrix. Many optimality criteria are based on this approximation of the covariance matrix. However, this approach underestimates the true covariance matrix of the parameters, and thus, the optimality criteria should be corrected in order to pay attention to the actual covariance. The bias in the estimation of the covariance matrix is negligible (or even null) for many models, and for this reason in those cases, it has no sense to deal with the corrected criteria because of the complexity of the calculations involved. But for some models, the correction does have importance, and thus, the modified criteria should be considered when designing; otherwise, the practitioner may risk to deal with poor designs. Some analytical results are presented for simpler models, and optimal designs taking into account the corrected variance will be computed and compared with those using the traditional approach for more complex models, showing that the loss in efficiency may be very important when the correction for the covariance matrix is ignored. Copyright © 2015 John Wiley & Sons, Ltd.     

Using Logistic Regression to Evaluate New Lid Designs

New product designs from competing vendors must often be evaluated in order to make the best decision on which design to use in manufacturing. In most cases, the designs must be challenged over a range of environmental factors, process tolerances, and incoming material variations. At times, the performance characteristic may take on the form of a passing or failing response. Due to the dichotomous nature of a pass/fail outcome, ordinary regression techniques based on a normal distribution of error terms with constant variance are not appropriate. In the case of a pass/fail response, a natural distribution to consider is the binomial distribution. The authors have exploited the field of generalized linear models, specifically logistic regression, to select a new lid design for a beverage container based on the correct distributional assumptions.     

半变系数模型约束PLS估计的渐近正态性

半变系数模型已经获得了广泛的研究和应用,近几年,人们提出许多方法来估计其函数系数和常系数.在PLS方法基础上,本文给出半变系数模型模型在线性随机约束条件下的估计,并证明了常系数和函数系数估计的渐近正态性.     

最优混料试验轴设计

混料试验设计被广泛地应用在工农业生产和科学研究中。本文讨论了三、四分量二阶可加混料模型的最优轴设计问题,使用对称的轴设计,获得了它们的轴设计类上的D-,A-最优轴设计。     

The Application of Random Balance Designs

In the chemical and petrochemical industries kinetic models are useful for describing the physical and chemical steps that occur in commercial processes. Often kinetic models involve several responses. Box and Draper (1965) have demonstrated that using multiresponse data for estimating the parameters in a model results in confidence regions for the parameters that are smaller than those obtained when the responses are considered individually, and they have developed a procedure for the multiresponse estimation of common parameters. Using multiresponse data also provides a better understanding of the reaction mechanism and makes possible a more comprehensive assessment of the correctness of the proposed model. Data from an oil shale pyrolysis experiment was used to fit and critique a sequence of models. These showed that conversion of the organic material in shale to oil was better explained when an intermediate product was included in the reaction network, and multiresponse techniques were employed. This led to a plausible kinetic representation of the pyrolysis process. Multiresponse models for more complex reaction mechanisms may require the estimation of a large number of parameters. An example is given, methods for minimizing computational difficulties in this situation are discussed, and some numerical results are presented.     

Considerations for D‐Optimal Sequential Design

Classical D‐optimal design is used to create experimental designs for situations in which an underlying system model is known or assumed known. The D‐optimal strategy can also be used to add additional experimental runs to an existing design. This paper demonstrates a study of variable choices related to sequential D‐optimal design and how those choices influence the D‐efficiency of the resulting complete design. The variables studied are total sample size, initial experimental design size, step size, whether or not to include center points in the initial design, and complexity of initial model assumption. The results indicate that increasing total sample size improves the D‐efficiency of the design, less effort should be placed in the initial design, especially when the true underlying system model isn't known, and it is better to start off with assuming a simpler model form, rather than a complex model, assuming that the experimenter can reach the true model form during the sequential experiments. Copyright © 2013 John Wiley & Sons, Ltd.     

Designs for Generalized Linear Models With Several Variables and Model Uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.