结构模型中预报方法的研究及其应用

本文对结构模型中未知真值在两种不同条件下的最佳预报方法进行了研究.其次,对因子模型预报方法进行了探讨.最后,分别举例说明了这些方法的应用.     

种群趋势指数的方差近似估计式及其应用

根据吴惠龙等（1986）发表的稻纵卷叶螟 Cnaphalocrocis medinalis 的生命表及 Watt 种群趋势指数数学模型,在delta-方法的基础上,本文提出了一种种群趋势指数方差的近似估计法,并应用于评价稻螟赤眼蜂Trichogramma japonicum Ashmead 及化学杀虫剂（甲六粉）对稻纵卷叶螟的控制作用。根据中心极限定律,当样本足够大时,种群趋势指数近似于正态分布。根据近似方差估计量以及 Z-检验方法,取得以下结论：放蜂区明显优于对照区,因其种群趋势指数取值较小,相应的 P 值为 0.0111,该区也明显优于化学杀虫剂处理区,相应的 P 值为 0.0036。杀虫剂处理区差于对照区,因其种群趋势指数值较大（0.3035）,但这种差异并未达到显著水平,P 值为 0.2236。虽然本文的结论近似于吴惠龙等（1986）单纯依据种群趋势指数所得到的结果,但本文的结论更具统计意义,更加可靠。     

单个协变量带有测量误差的多维结构回归模型

给出可交换条件下单个协变量的带有测量误差的多维结构回归模型,利用该模型研究总体平均处理效应的估计,给出当暴露组和对照组的协变量测量误差同分布时总体平均处理效应的拟极大似然估计及其性质.     

总体平均处理效应的拟极大似然估计

本文给出可交换条件下多维协变量的带有测量误差的多维结构回归模型,利用该模型研究总体平均处理效应的估计,给出当暴露组和对照组的协变量测量误差同分布时总体平均处理效应的拟极大似然估计及其性质．     

单种群生长的广义Logistic模型中参数的一种估值方法

本文提出种群生长的实测数据与广义Logistic模型的相容性条件,给出估计环境容纳量K的数学方法,利用常微分方程反问题的处理方法与麦夸特方法,对模型中参数进行近似估计与优化估计,其方法简便、通用性强．     

一种基于分布函数的基因数目估计方法

本文基于生物体性状的理论分布函数,提出一种新的基因（有效因子）数目估计方法。由于既考虑到了基因的加性作用,也包含了显性偏差和上位性偏差,使得理论分布函数能够较为全面地描述性状的实际分布。通过比较理论分与实测的经验分布,估计出控制该性状的基因数目。文章还讨论了估计方法的性质。应用新方法对许多例加以计算,并与Castle-Wright公式计算的结果比较,结果表明新方法明显优于Castle-Wright公式。     

非线性模型参数估计的一种新方法

本文以正交试验为工具,利用序贯思想,提出了非线性模型参数估计的正交试验法。该法简单易行,便于推广,且与Gauss-Newton法的结果相当。     

揭示群落结构及其环境响应的联合物种分布模型的研究进展

物种分布模型通常用于基础生态和应用生态研究,用来确定影响生物分布和物种丰富度的因素,量化物种与非生物条件的关系,预测物种对土地利用和气候变化的反应,并确定潜在的保护区.在传统的物种分布模型中,生物的相互作用很少被纳入,而联合物种分布模型(JSDMs)作为近年提出的一种新的可行方法,可以同时考虑环境因素和生物交互作用,因而成为分析生物群落结构和种间相互作用过程的有力工具.JSDMs以物种分布模型(SDMs)为基础,通常采用广义线性回归模型建立物种对环境变量的多变量响应,以随机效应的形式获取物种间的关联,同时结合隐变量模型(LVMs),并基于Laplace近似和马尔科夫蒙脱卡罗模拟的最大似然估计或贝叶斯方法来估算模型参数.本文对JSDMs的产生及理论基础进行归纳总结,重点介绍了不同类型JSDMs的特点及其在现代生态学中的应用,阐述了JSDMs的应用前景、使用过程中存在的问题及发展方向.随着对环境因素与多物种种间关系研究的深入,JSDMs将是今后物种分布模型研究的重点.     

Weibull分布参数辨识改进及对浙江毛竹林胸径年龄分布的测度

非线性模型迭代参数初始值的选取及拟合的结果能否可用非常重要且一直是一个难题.传统的方法只是凭感觉偿试不进行定量评估,对于用阻尼最小二乘进行拟合只注重精度高低,没有从理论上研究和分析评价得出的结果能否可用.为了克服这一不足,使参数选取较好,阻尼最小二乘得出结果可用.利用非线性回归原理在这两方面做了探讨,提出了二个判别指标：β^T＜1,β^N＜1,分析了每一指标在参数不同状态的控制作用,并在Weibull分布函数参数辨识中做了应用.针对目前毛竹林林分结构规律研究的不足,利用浙江省230个毛竹林样地资料研究了省域尺度的毛竹林胸径分布规律,经SPSS软件中的P-P图检验与柯尔莫哥洛夫检验,表明毛竹林胸径结构服从Weibull分布;再经对Weibull分布模型拟合求解与作图对比,结果显示Weibull分布能很好地描述毛竹林胸径分布规律.利用Weibull分布三参数与林分特征因子间的相关关系,经分析研究,导出了一个改进的二元分布模型,用该二元分布模型很好地测度了浙江省毛竹林胸径和年龄分布规律,最后得到了浙江省毛竹林株数按胸径年龄分布的理论频数.     

一种以准DOG分布为基元的体视匹配算法

本文提出了一种新体视的匹配算法,其特点是:(1)以准DOG分布为基元;(2)以同源性、唯一性、顺序性为约束;(3)本质上是一种协同算法。理论分析和实际计算表明,该算法是合理的,有效的。最近的一些心理物理学结果是支持我们的这个算法的。     

On an Unbiased Variance Estimator for the WILCOXON-MANN-WHITNEY-Statistic Based on Ranks

For some applications of the WILCOXON-MANN-WHITNEY-statistic its variance has to be estimated. So e.g. for the test of POTTHOFF (1963) to detect differences in medians of two symmetric distributions as well as for the computation of approximate, confidence bounds for the probability P(X₁ ≥ X₂), cf. GOVINDARAJULU (1968). In the present paper an easy to compute variance estimator is proposed which as only information uses the ranks of the data with the additional property that it is unbiased for the finite variance. Because of its invariance under any monotone transformation of the data its applicability is not confined to quantitative data. The estimator may be applied to ordinal data just as well. Some properties are discussed and a numerical example is given.     

Instrumental variable estimation of complier causal treatment effect with interval-censored data

Assessing causal treatment effect on a time-to-event outcome is of key interest in many scientific investigations. Instrumental variable (IV) is a useful tool to mitigate the impact of endogenous treatment selection to attain unbiased estimation of causal treatment effect. Existing development of IV methodology, however, has not attended to outcomes subject to interval censoring, which are ubiquitously present in studies with intermittent follow-up but are challenging to handle in terms of both theory and computation. In this work, we fill in this important gap by studying a general class of causal semiparametric transformation models with interval-censored data. We propose a nonparametric maximum likelihood estimator of the complier causal treatment effect. Moreover, we design a reliable and computationally stable expectation–maximization (EM) algorithm, which has a tractable objective function in the maximization step via the use of Poisson latent variables. The asymptotic properties of the proposed estimators, including the consistency, asymptotic normality, and semiparametric efficiency, are established with empirical process techniques. We conduct extensive simulation studies and an application to a colorectal cancer screening data set, showing satisfactory finite-sample performance of the proposed method as well as its prominent advantages over naive methods.     

Discrete Delta Estimation of the Variance of the Logistic Scores Estimator of ED50

A discrete delta method is applied to estimation of the standard error of the logistic scores estimator of ED50 in quantal bioassay. Results of a simulation study suggest that the standard error estimator is useful for assessing the precision of the ED50 estimate and for interval estimation of ED50.     

A New Estimator of the Discovery Probability

Summary Species sampling problems have a long history in ecological and biological studies and a number of issues, including the evaluation of species richness, the design of sampling experiments, and the estimation of rare species variety, are to be addressed. Such inferential problems have recently emerged also in genomic applications, however, exhibiting some peculiar features that make them more challenging: specifically, one has to deal with very large populations (genomic libraries) containing a huge number of distinct species (genes) and only a small portion of the library has been sampled (sequenced). These aspects motivate the Bayesian nonparametric approach we undertake, since it allows to achieve the degree of flexibility typically needed in this framework. Based on an observed sample of size n , focus will be on prediction of a key aspect of the outcome from an additional sample of size m , namely, the so‐called discovery probability. In particular, conditionally on an observed basic sample of size n , we derive a novel estimator of the probability of detecting, at the (n+m+1) th observation, species that have been observed with any given frequency in the enlarged sample of size n+m . Such an estimator admits a closed‐form expression that can be exactly evaluated. The result we obtain allows us to quantify both the rate at which rare species are detected and the achieved sample coverage of abundant species, as m increases. Natural applications are represented by the estimation of the probability of discovering rare genes within genomic libraries and the results are illustrated by means of two expressed sequence tags datasets.     

Maximum Likelihood Methods for Fitting the Burr Type XII Distribution to Life Test Data

This paper describes mathematical and computational methodology for estimating the parameters of the Burr Type XII distribution by the method of maximum likelihood. Expressions for the asymptotic variances and covariances of the parameter estimates are given, and the modality of the log-likelihood and conditional log-likelihood functions is analyzed. As a result of this analysis for various a priori known and unknown parameter combinations, conditions are given which guarantee that the parameter estimates obtained will, indeed, be maximum likelihood estimates. An efficient numerical method for maximizing the conditional log-likelihood function is described, and mathematical expressions are given for the various numerical approximations needed to evaluate the expressions given for the asymptotic variances and covariances of the parameter estimates. The methodology discussed is applied in a numerical example to life test data arising in a clinical setting.     

Efficiency of the Sample Variance for the Lognormal Distribution

Two unbiased estimators T and ?? of the variance ? = var (Y) of a lognormal distribution are considered. Here T is the sample variance and ?? is the minimum variance unbiased estimator of ?. The values of the ratio E = 100 var (??)/var (T) are tabulated for some values of the sample size n and of the coefficient of variation δ.     

A Nonparametric Estimator of Heterogeneity Variance with Applications to SMR‐ and Proportion‐Data

In this paper the situation of extra population heterogeneity is discussed from a analysis of variance point of view. We first provide a non‐iterative way of estimating the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself for Poisson and binomial counts. The consequences of the presence of heterogeneity in the estimation of the mean are discussed. We show that if the homogeneity assumption holds, the pooled mean is optimal while in the presence of strong heterogeneity, the simple (arithmetic) mean is an optimal estimator of the mean SMR or mean proportion. These results lead to the problem of finding an optimal estimator for situations not represented by these two extreme cases. We propose an iterative solution to this problem. Illustrations for the application of these findings are provided with examples from various areas.