H广义线性模型中的参数估计的比较

本文研究H广义线性模型中未知参数的两种估计方法,一种是边际似然函数法,另一种是Lee和Nelder提出来的L-N法．对于一类具有两个随机效应的典型的Poisson-Gamma类模型,在一些正则性条件之下,我们已经证明了其中固定效应卢的L-N估计的强相合性及渐近正态性,并得到了其收敛于真值的速度．针对这类模型,本文进一步给出了其边际似然函数的解析表达式,并且通过Monte Carlo模拟,对模型中固定效应β的边际似然估计和L—N估计进行了比较,模拟表明L—N估计比边际似然估计在拟Poisson-Gamma模型中有着更加优良的表现,具有更高的精度。     

一个血吸虫病数学模型的交替方向有限元分析

摘要：对血吸虫病数学模型利用交替方向Galerkin方法逼近模型(P)的解,并利用微分方程先验估计理论和技巧,进行近似解的收敛性分析,得到其最优L^2模误差估计．     

具有亲缘关系矩阵的混合模型的方差组分迭代估计——应用于计算BLUP的方差比值和遗传参数

论述的是来自非均街资料的混合模型中具有亲缘关系矩阵时利用迭代法估计方差组分问题。这篇文章表明计算程序是可行的,只要能够按照混合模型中固定效应的结构矩阵和Henderson方法3的固定效应的假设条件正确地计算二次型约化平方和,就可获得较为精确的方差组分估计值;而且表明方差初始比值k偏高或偏低,不影响迭代求解的最后结果,这是因为在迭代过程中可以通过结构矩阵x'x和x'x的控制而自行调整。这些方差组分不仅可应用于选种种畜用的BLUP计算,还可用来估计遗传参数。     

基准剂量软件BMDS中连续模型的研究

对美国环境保护署开发的基准剂量软件BMDS的2.1.1版中连续模型进行了剖析,详细介绍了模型形式;参数初始值的设置、估计方法、标准误、置信上下限;全模型、残差模型和拟合模型的对数似然函数、模型的显著性检验;各剂量下概率的预测、残差;两种风险模式下基准剂量的计算方法,并将计算结果与BMDS软件的计算结果进行比较,结果表明本文介绍的计算方法的正确性,为下一步进行软件设计奠定了理论基础.     

基于冠层温湿度模型的日光温室黄瓜霜霉病预警方法

利用温室环境参数构建室内微环境模拟模型,并结合温室病害模型进行预警,便于开展病害生态防治,以减少农药使用,从而保护温室生态环境和保证农产品质量安全.本文利用温室内能量守恒原理和水分平衡原理,构建了日光温室冠层叶片温度和空气相对湿度模拟模型.叶片温度模拟模型考虑了温室内植物与墙体、土壤、覆盖物之间的辐射热交换,以及室内净辐射、叶片蒸腾作用引起的能量变化;相对湿度模拟模型综合了温室内叶片蒸腾、土壤蒸发、覆盖物与叶面的水汽凝结引起的水分变化.将温湿度估计模型输出值作为参数,输入黄瓜霜霉病初侵染和潜育期预警模型中,估计黄瓜霜霉病发病日期,并与田间观测的实际发病日期比较.试验选取2014年9月和10月的温湿度监测数据进行模型验证,冠层叶片温度实际值与模拟值的均方根偏差（RMSD)分别为0.016和0.024 ℃,空气相对湿度实际值与模拟值的RMSD分别为0.15%和0.13%.结合温湿度估计模型结果表明,黄瓜病害预警系统预测黄瓜霜霉病发病日期与田间调查发病日期相吻合.本研究可为黄瓜日光温室病害预警模型及系统构建提供微环境数据支持.     

关于广义Potthoff—Roy估计

本文考察了生长曲线模型的定义形式,并因此建立了相应的广义Potthoff-Roy估计,在最小范数准则下,给出了估计的最佳选择并且讨论了协变量以及改进估计的方法,尤其当设计阵病态时,给出了两类新的岭型Potthoff-Roy估计。     

一个推广增长曲线模型协差阵的最小二乘估计及其优良性

在准正态情形与独立同分布情形下,分别给出了一个推广增长曲线模型中协差阵的最小二乘估计,并得到了最小二乘估计成为一致最小方差不变二次无偏估计的充要条件．     

利用多重抽样估计稀有物种的种类数

利用矩估计和二个稳健估计方法（jackknife估计,bootstrap估计）来处理野外生态学工作者的调查数据,在假定已经发现一些稀有物种的情形下,通过统计推断得到那些未被发现的物种的种类数。利用本文所提出的方法调查水稻水稻田的昆虫群落和林地的在面植被群落的稀有种是十分有效的。     

多QTL定位的压缩估计方法

本文综述了多标记分析和多QTL定位的压缩估计方法。对于前者,Xu（Genetics,2003,163：789—801）首先提出了Bayesian压缩估计方法。其关键在于让每个效应有一个特定的方差参数,而该方差又服从一定的先验分布,以致能从资料中估计之。由此,能够同时估计大量分子标记基因座的遗传效应,即使大多数标记的效应是可忽略的。然而,对于上位性遗传模型,其运算时间还是过长。为此,笔者将上述思想嵌入极大似然法,提出了惩罚最大似然方法。模拟研究显示：该方法能处理变量个数大于样本容量10倍左右的线性遗传模型。对于后者,本文详细介绍了基于固定区间和可变区间的Bayesian压缩估计方法。固定区间方法可处理中等密度的分子标记资料;可变区间方法则可分析高密度分子标记资料,甚至是上位性遗传模型。对于上位性检测,已介绍的惩罚最大似然方法和可变区间Bayesian压缩估计方法可供利用。应当指出,压缩估计方法在今后的eQTL和QTN定位以及基因互作网络分析等研究中也是有应用价值的。     

物种总数的一类Bayes区间估计的改进

通常所使用的由传统方法得到的物种总数的一类Bayes置信区间不是最短的,就此意义而言也不是最优的。本文得到改进后的Bayes区间估计,并在各种有代表性的自由度情形下通过对比指出它相对于传统的Bayes区间估计的优越性所在,由分析可见,改进后的区间估计更能满足生产实践的需要,得到的物种总数的区间估计更为精确。     

Abundance Estimation With a Transient Model Under the Robust Design

Abstract: A common situation in capture-mark-recapture (CMR) studies on birds and other organisms is to capture individuals not belonging to the studied population only present during the short time of the capture session. Presence of such transient individuals affects demographic parameter estimation from CMR data. Methods exist to reduce biases on survival estimates in the presence of transients and have been shown to be particularly efficient within the Robust Design framework (several secondary capture sessions within a short time interval during which the studied population can be assumed closed). We present a new model to estimate population size accounting for transients. We first used simulated data to show that the method reduces positive biases due to transients. In a second step, we applied the method to a real CMR dataset on a reed warbler (Acrocephalus scirpaceus) population. Population size estimates are reduced by up to 50% when correcting for the presence of transients. Many field studies on managed animal populations use capture-recapture methodology to obtain crucial parameters of the focal population demography. The resulting data sets are used either to estimate population size ignoring the presence of transients, or to estimate vital rates, accounting for transients but overlooking abundance estimation. Our method conciliates these 2 approaches.     

Two‐stage orthogonality based estimation for semiparametric varying‐coefficient models and its applications in analyzing AIDS data

Semiparametric smoothing methods are usually used to model longitudinal data, and the interest is to improve efficiency for regression coefficients. This paper is concerned with the estimation in semiparametric varying‐coefficient models (SVCMs) for longitudinal data. By the orthogonal projection method, local linear technique, quasi‐score estimation, and quasi‐maximum likelihood estimation, we propose a two‐stage orthogonality‐based method to estimate parameter vector, coefficient function vector, and covariance function. The developed procedures can be implemented separately and the resulting estimators do not affect each other. Under some mild conditions, asymptotic properties of the resulting estimators are established explicitly. In particular, the asymptotic behavior of the estimator of coefficient function vector at the boundaries is examined. Further, the finite sample performance of the proposed procedures is assessed by Monte Carlo simulation experiments. Finally, the proposed methodology is illustrated with an analysis of an acquired immune deficiency syndrome (AIDS) dataset.     

普通克立格法在昆虫生态学中的应用

地统计学是以区域化变量为基础,以变差函数为主要工龄,分析空间相关变量结构的统计方法。在对波动较大的实验变差函数进行拟合时,虽无法获得最优拟合,但运用人机对话的拟合方法来灵活选取参数,可以得到较理想的变差函数模型的参数。本文运用加权多项式回归法以及人机对话的方法,得到了较理想的1级与2级球状模型拟合结果,同时利用直线函数对实验变差函数进行了拟合,最后利用普通Kriging法,对待估计点进行各理论模型的最优、线性、无偏内插估计,得出克立格内插权重。将此方法应用于广东省四会市大沙镇富溪乡试验田稻飞观测数据,由待估点周围若干观测点的数据,有效地估计出待估点的昆虫分布密度,并讨论比较了不同理论模型的拟合效果以及估计误差。结果表明,2级球状模型的拟合最好,一级球状模型次之,直线函数的拟合最差,但直线函数计算最为简便。     

Unbiased estimation of selected treatment means in two-stage trials

Straightforward estimation of a treatment's effect in an adaptive clinical trial can be severely hindered when it has been chosen from a larger group of potential candidates. This is because selection mechanisms that condition on the rank order of treatment statistics introduce bias. Nevertheless, designs of this sort are seen as a practical and efficient way to fast track the most promising compounds in drug development. In this paper we extend the method of Cohen and Sackrowitz (1989) who proposed a two-stage unbiased estimate for the best performing treatment at interim. This enables their estimate to work for unequal stage one and two sample sizes, and also when the quantity of interest is the best, second best, or j -th best treatment out of k. The implications of this new flexibility are explored via simulation.     

Estimation of capture probabilities using generalized estimating equations and mixed effects approaches

Modeling individual heterogeneity in capture probabilities has been one of the most challenging tasks in capture–recapture studies. Heterogeneity in capture probabilities can be modeled as a function of individual covariates, but correlation structure among capture occasions should be taking into account. A proposed generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) approaches can be used to estimate capture probabilities and population size for capture–recapture closed population models. An example is used for an illustrative application and for comparison with currently used methodology. A simulation study is also conducted to show the performance of the estimation procedures. Our simulation results show that the proposed quasi‐likelihood based on GEE approach provides lower SE than partial likelihood based on either generalized linear models (GLM) or GLMM approaches for estimating population size in a closed capture–recapture experiment. Estimator performance is good if a large proportion of individuals are captured. For cases where only a small proportion of individuals are captured, the estimates become unstable, but the GEE approach outperforms the other methods.     

Numerical non-identifiability regions of the minimal model of glucose kinetics: superiority of Bayesian estimation

The so-called minimal model (MM) of glucose kinetics is widely employed to estimate insulin sensitivity (S(I)) both in clinical and epidemiological studies. Usually, MM is numerically identified by resorting to Fisherian parameter estimation techniques, such as maximum likelihood (ML). However, unsatisfactory parameter estimates are sometimes obtained, e.g. S(I) estimates virtually zero or unrealistically high and affected by very large uncertainty, making the practical use of MM difficult. The first result of this paper concerns the mathematical demonstration that these estimation difficulties are inherent to MM structure which can expose S(I) estimation to the risk of numerical non-identifiability. The second result is based on simulation studies and shows that Bayesian parameter estimation techniques are less sensitive, in terms of both accuracy and precision, than the Fisherian ones with respect to these difficulties. In conclusion, Bayesian parameter estimation can successfully deal with difficulties of MM identification inherently due to its structure.     

An adaptive neuro-fuzzy method (<Emphasis Type="Italic">ANFIS</Emphasis>) for estimating single-trial movement-related potentials

This study aims to recover transient, trial-varying evoked potentials (EPs), in particular the movement-related potentials (MRPs), embedded within the background cerebral activity at very low signal-to-noise ratios (SNRs). A new adaptive neuro-fuzzy technique will attempt to estimate movement-related potentials within multi-channel EEG recordings, enabling this method to completely adapt to each input sweep without system training procedures. We assume that one of the sensors is corrupted by noise deriving from other sensors via an unknown function that will be estimated. We will approach this problem by: (1) spatially decorrelating the sensors in the preprocessing phase, (2) choosing the most informative of the filtered channels that will permit the best MRP estimation (input-selection phase) and (3) training the neuro-fuzzy model to fit the noise over the chosen sensor and therefore estimating the buried MRP. We tested this framework with simulations to validate the analytical results before applying them to the real biological data. Whenever it is applied to biological data, this method improves the SNR by more than 12dB, even to very low SNRs. The processing method proposed here is likely to complement other estimation techniques and can be useful to process, enhance and analyse single-trial MRPs.     

A diagnostic for Cox regression with discrete failure-time models

Changes in maximum likelihood parameter estimates due to deletion of individual observations are useful statistics, both for regression diagnostics and for computing robust estimates of covariance. For many likelihoods, including those in the exponential family, these delete-one statistics can be approximated analytically from a one-step Newton-Raphson iteration on the full maximum likelihood solution. But for general conditional likelihoods and the related Cox partial likelihood, the one-step method does not reduce to an analytic solution. For these likelihoods, an alternative analytic approximation that relies on an appropriately augmented design matrix has been proposed. In this paper, we extend the augmentation approach to explicitly deal with discrete failure-time models. In these models, an individual subject may contribute information at several time points, thereby appearing in multiple risk sets before eventually experiencing a failure or being censored. Our extension also allows the covariates to be time dependent. The new augmentation requires no additional computational resources while improving results.     

Estimating subject-specific body segment parameters using a 3-dimensional modeller program

The estimation of body segment properties is important in the biomechanical analysis of movement. Current subject-specific estimation methods however can be expensive and time-consuming, while other methods do not adequately take into account individual or group variability. We describe a simple procedure for estimating subject-specific geometric properties, independent of joint centres. The method requires only a small number of anthropometric measurements and digital images of the segment or subject, a 3-dimensional modeller program and simple mathematical calculations to estimate segment volumes and centroids. Assuming that the segment is of uniform density, it's mass and moment of inertia can also be derived. Future work should include generating segment density profiles for particular populations, to increase the accuracy of the method, and comparing the accuracy of the results obtained with those produced by other techniques.     

Efficient statistical inference procedures for partially nonlinear models and their applications

Summary .   Motivated by an analysis of a real data set in ecology, we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present. We develop two new estimation procedures to estimate the parameters in the parametric component. Consistency and asymptotic normality of the resulting estimators are established. We further propose an estimation procedure and a generalized F -test procedure for the nonparametric component in the partially nonlinear models. Asymptotic properties of the newly proposed estimation procedure and the test statistic are derived. Finite sample performance of the proposed inference procedures are assessed by Monte Carlo simulation studies. An application in ecology is used to illustrate the proposed methods.