删失数据下非线性半参数回归模型中参数的经验似然推断

考察了响应变量在随机删失情形下的非线性半参数回归模型,构造了未知参数的经验对数似然比统计量和调整经验对数似然比统计量,证明在一定条件下,所构造的经验似然比统计量渐近于X~2分布,并由此构造出未知参数的置信域.此外,又构造了未知参数的最小二乘估计量,证明了它的渐近性质.通过模拟研究表明,经验似然方法在置信域的覆盖概率以及精度方面要优于最小二乘法.     

稀有变异遗传关联性研究中常用负担检验方法比较

为比较稀有变异遗传关联研究中常用负担检验方法(CMC、WST、SUM及其扩展)在不同遗传情境下的统计性能,本文通过计算机模拟产生不同样本量、连锁不平衡(linkage disequilibrium, LD)参数、混杂非关联变异的个数和不同效应的关联变异等条件的稀有变异病例对照数据集,运用各种负担检验方法进行分析,分别计算各方法的一类错误和效能。结果表明,各方法一类错误均在0.05附近;当稀有变异效应方向一致时,除aSUM法外,LD参数越大、混杂非关联变异越少、各法效能越高;当效应方向不一致时,各法效能则显著降低。除强LD外,有方向考虑的方法效能均比无方向考虑的方法高,且样本量越大效能越高。负担检验的统计性能受效应大小和方向、噪音变异和连锁不平衡等多种因素影响。在实际应用中,在各类方法选择、确定集合单位,权重等时最好结合遗传变异的生物信息先验以提高研究效能。     

农业生产中四组数据的Logistic模型的参数确定

本文介绍了求非线性回归模型参数的基本理论,选择Logistic回归模型作为模型函数.以牧草再生长的数据集1为例,用Mathematica软件绘制了数据集1的点图.最后给出四组数据的拟合曲线和置信域.     

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.     

中域效应模型中物种分布幅度梯度的影响

中域效应（Mid-domain effect）模型量化了几何限制对物种丰富度空间分布格局的影响．然而,目前的研究缺乏对该模型的生物学意义作进一步的阐明,以及对物种分布幅度的梯度变化进行数量评价．本文利用已发表的马达加斯加蝴蝶的多样性数据,通过模拟方法和物种幅度频度分布（RSFD）的分析,研究了几何限制和物种幅度非随机分布的共同效应．研究发现,尽管马达加斯加蝴蝶物种丰富度的分布格局满足中域效应模型,但并不符合该模型的特征RSFD变化．如果在模型中加入物种分布幅度的梯度变化,则能较好地模拟实际RSFD的变化,表明物种丰富度的空间格局确实存在物种分布幅度的梯度变化．同时还发现,物种分布幅度梯度的存在对最终丰富度格局影响不大,表明中域效应模型的生物学意义难以从物种分布幅度的行为上来解释．     

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.     

家蚕微粒子病母蛾序贯抽样检验方法研究

本文根据统计学理论,设计了一套家蚕微粒子病母蛾序贯抽样检验方案,用此方案进行的抽样检验,不仅保证了将不合格蚕种判为合格蚕种的概率控制在1.5％以内,而且大大减少了将合格蚕种判为不合格蚕种的概率．并且镜检蛾数一般随总体病蛾率ρ而变化。当ρ较低或较高（相对于0.5％）时,需检验的数量就较少.本方案的实际检验工作量并未比现行检验方案有明显增加.     

叶片结构对跑道池式光生物反应器功耗及混合性能影响的数值模拟

跑道池式光生物反应器中的叶轮叶片形状对于藻液的混合效果和反应器的功耗有很大的影响,利用计算流体力学方法对某后折型叶片的结构参数进行了优化,首先通过流动模拟的结果和已有的实验数据的对比,验证了模拟方法及模型的可靠性,随后运用响应面分析方法综合分析了两个叶片结构参数(叶片弯折比L_1/L_2和叶片弯折角α)对该反应器单位功耗光梯度方向上混合性能的影响。结果表明,当L_1/L_2等于1,且α等于90°时,反应器单位功耗混合性能参数η呈最大值,即在此叶片结构参数下,当叶轮输入功率一定时,该反应器内部藻液光梯度方向上的混合性能最好,对比未改变叶片结构参数情况下的跑道池式光生物反应器,其η值增大到2.64倍。     

岷江上游干旱河谷农林边界影响域的研究

对岷江上游农林边界的影响域进行研究,以提高该区管理农田和林地的水平．共调查3种类型农林边界10条样带,采用移动窗口法对植物多样性的数据进行分析,结果表明,当窗口宽度达到6～10时。SED曲线的变化趋向稳定,并且在曲线上有一或两个峰值出现．不同类型边界的影响域是不同的,但均在距边界50m内．各类型边界的影响域多在12～30m之间．6条林地样带只有M2和M6样带林地的影响域被确定,而4条农田样带的影响域均被确定．影响域的大小取决于边界两侧斑块类型和地形以及小气候等因子,但坡向对其影响不大;移动窗口法能有效地刻画边界动态,是一种分析边界简单而有力的工具．这些结果有利于进一步理解干旱河谷区农林间的相互作用．     

基于最大熵原理的浙江毛竹胸径分布及测量不确定度评定

应用最大熵原理构造了测树因子概率分布的统一模型,这样构造的模型具有明确的解析表达式,并能克服常用方法无法解释测树因子服从某种概率分布的真正原因,从而为测树因子统计分布建模提供了一种有效方法.使用1-3阶样本矩、1-4阶样本矩与1-5阶样本矩,用所构建的概率分布统一模型分别对浙江省域毛竹胸径分布分别作了仿真试验,结果表明当采用1-4阶样本矩时,仿真效果最好,而且比通过假设检验的Weibull分布仿真结果理想:(1)图形非常相似,对实测数据都能很好的模拟;(2)最大熵法的离差平方和为0.00018,Weibull分布的为0.00045[1].由于各种系统与非系统的原因,都会影响测量结果的准确性,对所构建的模型作了不确定度评定,表明结果具有很大的可靠性,测量结果的估计:7.85100,测量结果的标准不确定度:1.82710,置信概率:0.96020.     

Unconditional small-sample confidence intervals for the odds ratio

The traditional approach to 'exact' small-sample interval estimation of the odds ratio for binomial, Poisson, or multinomial samples uses the conditional distribution to eliminate nuisance parameters. This approach can be very conservative. For two independent binomial samples, we study an unconditional approach with overall confidence level guaranteed to equal at least the nominal level. With small samples this interval tends to be shorter and have coverage probabilities nearer the nominal level.     

On small-sample confidence intervals for parameters in discrete distributions

The traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level. In constructing such intervals for parameters in discrete distributions, less conservative behavior results from inverting a single two-sided test than inverting two separate one-sided tests of half the nominal level each. We illustrate for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio.     

Confidence intervals for directly standardized rates using mid‐p gamma intervals

Directly standardized rates continue to be an integral tool for presenting rates for diseases that are highly dependent on age, such as cancer. Statistically, these rates are modeled as a weighted sum of Poisson random variables. This is a difficult statistical problem, because there are k observed Poisson variables and k unknown means. The gamma confidence interval has been shown through simulations to have at least nominal coverage in all simulated scenarios, but it can be overly conservative. Previous modifications to that method have closer to nominal coverage on average, but they do not achieve the nominal coverage bound in all situations. Further, those modifications are not central intervals, and the upper coverage error rate can be substantially more than half the nominal error. Here we apply a mid‐p modification to the gamma confidence interval. Typical mid‐p methods forsake guaranteed coverage to get coverage that is sometimes higher and sometimes lower than the nominal coverage rate, depending on the values of the parameters. The mid‐p gamma interval does not have guaranteed coverage in all situations; however, in the (not rare) situations where the gamma method is overly conservative, the mid‐p gamma interval often has at least nominal coverage. The mid‐p gamma interval is especially appropriate when one wants a central interval, since simulations show that in many situations both the upper and lower coverage error rates are on average less than or equal to half the nominal error rate.     

Conditional Maximum Likelihood Estimate and Exact Test of the Common Relative Difference in Combination of 2 × 2 Tables under Inverse Sampling

On the basis of the conditional distribution, given the marginal totals of non-cases fixed for each of independent 2 × 2 tables under inverse sampling, this paper develops the conditional maximum likelihood (CMLE) estimator of the underlying common relative difference (RD) and its asymptotic conditional variance. This paper further provides for the RD an exact interval calculation procedure, of which the coverage probability is always larger than or equal to the desired confidence level and for investigating whether the underlying common RD equals any specified value an exact test procedure, of which Type I error is always less than or equal to the nominal α-level. These exact interval estimation and exact hypothesis testing procedures are especially useful for the situation in which the number of index subjects in a study is small and the asymptotically approximate methods may not be appropriate for use. This paper also notes the condition under which the CMLE of RD uniquely exists and includes a simple example to illustrate use of these techniques.     

A New Distribution-Free Approach to Constructing the Confidence Region for Multiple Parameters

Construction of confidence intervals or regions is an important part of statistical inference. The usual approach to constructing a confidence interval for a single parameter or confidence region for two or more parameters requires that the distribution of estimated parameters is known or can be assumed. In reality, the sampling distributions of parameters of biological importance are often unknown or difficult to be characterized. Distribution-free nonparametric resampling methods such as bootstrapping and permutation have been widely used to construct the confidence interval for a single parameter. There are also several parametric (ellipse) and nonparametric (convex hull peeling, bagplot and HPDregionplot) methods available for constructing confidence regions for two or more parameters. However, these methods have some key deficiencies including biased estimation of the true coverage rate, failure to account for the shape of the distribution inherent in the data and difficulty to implement. The purpose of this paper is to develop a new distribution-free method for constructing the confidence region that is based only on a few basic geometrical principles and accounts for the actual shape of the distribution inherent in the real data. The new method is implemented in an R package, distfree.cr/R. The statistical properties of the new method are evaluated and compared with those of the other methods through Monte Carlo simulation. Our new method outperforms the other methods regardless of whether the samples are taken from normal or non-normal bivariate distributions. In addition, the superiority of our method is consistent across different sample sizes and different levels of correlation between the two variables. We also analyze three biological data sets to illustrate the use of our new method for genomics and other biological researches.     

The empirical coverage of confidence intervals: Point estimates and confidence intervals for confidence levels

Many confidence intervals calculated in practice are potentially not exact, either because the requirements for the interval estimator to be exact are known to be violated, or because the (exact) distribution of the data is unknown. If a confidence interval is approximate, the crucial question is how well its true coverage probability approximates its intended coverage probability. In this paper we propose to use the bootstrap to calculate an empirical estimate for the (true) coverage probability of a confidence interval. In the first instance, the empirical coverage can be used to assess whether a given type of confidence interval is adequate for the data at hand. More generally, when planning the statistical analysis of future trials based on existing data pools, the empirical coverage can be used to study the coverage properties of confidence intervals as a function of type of data, sample size, and analysis scale, and thus inform the statistical analysis plan for the future trial. In this sense, the paper proposes an alternative to the problematic pretest of the data for normality, followed by selection of the analysis method based on the results of the pretest. We apply the methodology to a data pool of bioequivalence studies, and in the selection of covariance patterns for repeated measures data.     

Improved exact confidence intervals for the odds ratio in two independent binomial samples

For two independent binomial samples, the usual exact confidence interval for the odds ratio based on the conditional approach can be very conservative. Recently, Agresti and Min (2002) showed that the unconditional intervals are preferable to conditional intervals with small sample sizes. We use the unconditional approach to obtain a modified interval, which has shorter length, and its coverage probability is closer to and at least the nominal confidence coefficient.     

Estimating the immunity coverage required to prevent epidemics in a community of households

An estimation of the immunity coverage needed to prevent future outbreaks of an infectious disease is considered for a community of households. Data on outbreak size in a sample of households from one epidemic are used to derive maximum likelihood estimates and confidence bounds for parameters of a stochastic model for disease transmission in a community of households. These parameter estimates induce estimates and confidence bounds for the basic reproduction number and the critical immunity coverage, which are the parameters of main interest when aiming at preventing major outbreaks in the future. The case when individuals are homogeneous, apart from the size of their household, is considered in detail. The generalization to the case with variable infectivity, susceptibility and/or mixing behaviour is discussed more briefly. The methods are illustrated with an application to data on influenza in Tecumseh, Michigan.     

A note on the conditional approach to interval estimation in the calibration problem.

In the calibration problem, the need to construct a confidence interval to estimate the unknown chi 0 arises when the null hypothesis of zero slope is rejected. Otherwise, the resulting confidence interval will be infinite to reflect the fact that the slope of the regression line may be zero. Under the condition of rejecting the hypothesis of zero slope, we study the properties of the conditional coverage rate of the calibration confidence interval. The conditional coverage rate (P1) is a function of the slope, distance between chi 0 and the mean of the trailing sample means, the sum of squares of chi, and n. When the true slope is close to 0 and chi 0 is away from means, P1 can go down to 0. On the other hand, as the power of testing zero slope reaches 1, with or without chi 0 close to means, P1 will tend to the desired nominal coverage rate. In summary, one should choose a reasonably small alpha in testing zero slope to avoid constructing a confidence interval for chi 0 when the true slope is 0. In addition, it is desirable to have high power in testing zero slope so that the resulting confidence interval will maintain the desired coverage rate when using the conditional approach in the calibration problem.     

Interval estimation of the LD50 based on an up-and-down experiment

It is well known that an up-and-down method can be more efficient than fixed-sample methods in estimating the LD50 of a quantal response curve. A problem that has not been addressed by many is that of obtaining a confidence interval for the LD50 from the up-and-down method. Dixon and Mood (1948, Journal of the American Statistical Association 43, 109-126) proposed a confidence interval using a maximum likelihood approach, but not much is known about its properties. In this paper, a new confidence interval for the LD50 based on turning points is obtained, which uses the concept of phi-mixing. Simulation results indicate that the coverage probabilities of both methods tend to be less than the nominal level unless the sample size is large. Even so, when the tolerance distribution is normal, the proposed confidence interval is found to be superior to Dixon's interval in terms of the coverage, the width, and stability. The advantages of the method do not appear to hold in the presence of nonnormal tolerance distribution.