二项分布下基于鞍点逼近的总体成数置信区间的构造

面对总体成数置信区间的估计问题,可以采用二项分布下基于鞍点逼近的方法来构造总体成数的置信区间,这种方法为总体成数的区间估计提供了一种新的途径,将其和传统的区间估计方法比较,即正态近似法和枢轴量法进行比较。蒙特卡洛模拟和实例分析的结果为:在几种不同的置信区间构造方法中,小样本情况下,鞍点逼近方法构造的总体成数的置信区间长度相对较短,覆盖率最接近名义水平;大样本下,鞍点逼近方法整体表现最优。因此,可以得到鞍点逼近法对总体成数置信区间的估计较为精确,尤其是小样本情况下更为适用的结论。     

双参数指数分布尺度参数的区间估计

基于残缺的样本观测数据,文章讨论了双参数指数分布总体尺度参数的区间估计问题.给出了适用于残缺观测数据的构造置信区间的一种新方法,讨论了枢轴量的精确分布和大样本近似分布,得到了尺度参数的近似置信区间.这个结果还适用于样本中可能存在异常数据的情形,具有稳健性.     

零浮动Poisson项目计数法在敏感数据抽样调查中的应用

文章将Poisson-Poisson项目计数法进行推广,提出零浮动Poisson项目计数法,其中,非敏感辅助变量来自于一个参数已知的零浮动Poisson分布。并给出了该模型下敏感参数极大似然估计的EM算法以及构造其置信区间的bootstrap方法。此外,还对该模型保护受访者隐私的能力加以讨论,发现该模型的隐私保护要优于Poisson-Poisson项目计数法。最后,从随机模拟的结果表明在该模型下利用本文所介绍的分析方法可以得到敏感参数的较为准确的估计。     

不完全数据场合下双参数指数分布参数的区间估计

文章讨论了双参数指数分布参数基于不完全数据情况下的置信区间的构造问题.针对门限参数和尺度参数,分别给出了用于构造置信区间的枢轴量,讨论了门限参数的枢轴量以及尺度参数的枢轴量的精确分布,得到了相应的置信区间.针对尺度参数置信区间构造的枢轴量可以抵抗样本中异常数据的干扰,具有一定程度的稳健性.     

逆Weibull分布参数的点估计和联合置信域估计

文章基于完全样本,针对两参数逆Weibull分布参数的点估计和置信区间估计问题,利用二分法导出了参数的最大似然估计,但最大似然估计法不能给出参数的精确置信区间估计,通过构造一类枢轴量得到了形状参数的精确置信区间估计,同时给出了形状参数和尺度参数的联合置信域估计。     

Polya后验方法在有限总体抽样估计中的模拟研究

polya后验方法作为一种无信息贝叶斯估计方法,在有限总体抽样中,通过观测的样本,构造一系列的模拟总体,然后进行统计推断。通过统计模拟研究了polya后验方法估计的一些特点,并和Bootstrap方法进行比较。模拟结果显示:polya后验方法能够很好地估计总体的均值,随着样本量的增大,估计值与真值的差距越来越小。采用polya后验方法构造的置信区间区间长度较小,能够很好地覆盖真值。     

异方差下多个正态总体共同均值的参数bootstrap推断

文章使用参数bootstrap (PB)方法考虑了当方差未知且可以不相等时多个正态总体共同均值的假设检验和置信区间构造问题.基于共同均值一个著名估计,提出了一种参数bootstrap统计推断方法,并借助Mon-te Carlo方法与经典的近似解法和广义推断方法进行了比较.随机模拟结果表明,就第一类错误概率和覆盖率而言,参数bootstrap推断方法表现更好.参数bootstrap方法不仅具有满意的第一类错误概率和覆盖率,而且具有良好的检验功效和置信区间平均长度表现.     

负相协样本下总体分位数的经验似然渐近性质的推断

文章在强平稳负相协样本下,利用分组经验似然比方法,克服了传统经验似然方法的缺陷,所得到的渐近分布为标准的卡方分布,便于构造总体分位数的渐近置信区间.     

正态线形模型下缺失值的Bootstrap多重插补与比较

缺失值是调查中普遍存在的问题,对缺失值进行插补是处理缺失值的较好方法.如果变量之间存在相关关系,可以通过正态线形模型利用不存在缺失值的变量对有存在缺失值的变量进行插补.较之单一插补,多重插补更能有效地估计总体方差,因此更多地被使用.文章借助Bootstrap法,让模型的参数和残差来自完全观测的Bootstrap样本的最小平法估计,可进一步准确估计总体方差.通过大量模拟试验,发现Bootstrap多重插补较之单一插补和一般多重插补能构建更宽的置信区间从而有更准确的总体参数覆盖率,这点在数据缺失比重很大时优势更明显.     

简单均匀分布参数同等最短置信区间的求法

对形如U(0,θ)的均匀分布,文章在给定置信水平1-a下,用计算函数极值的方法得到了参数q的平均长度最短的同等置信区间,然后通过最大密度区间法得到了该参数的相同的最短置信区间,后者的求解过程也充分印证了该方法也是确定参数最短置信区间以及构造等尾置信区间的依据.     

Max-min multiple comparison procedure for comparing several dose levels with a zero dose control

The comparison of increasing doses of a compound to a zero dose control is of interest in medical and toxicological studies. Assume that the mean dose effects are non-decreasing among the non-zero doses of the compound. A simple procedure that modifies Dunnett's procedure is proposed to construct simultaneous confidence intervals for pairwise comparisons of each dose group with the zero dose control by utilizing the ordering of the means. The simultaneous lower bounds and upper bounds by the new procedure are monotone, which is not the case with Dunnett's procedure. This is useful to categorize dose levels. The expected gains of the new procedure over Dunnett's procedure are studied. The procedure is shown by real data to compare well with its predecessor.     

Exact intervals and tests for mean of symmetrical population when one "sample" value possibly an outlier

The (continuous) data are n observations that are believed to be a random sample from a symmetrical population. Confidence intervals and significance tests for the population mean are desired. There is, however, the possibility that either the smallest observation or the largest observation is an outlier. That is, the population providing this observation differs from the symmetrical population providing the other n - 1 observations. If this occurs, intervals and tests are desired for the mean of the population providing the other n - 1 observations. Some investigation difficulties can be overcome if intervals and tests can be developed that are simultaneously usable for all of these three situations (a confidence coefficient, or significance level, has the same value for all three situations). Two kinds of intervals and tests with this property are developed. These results always involve both the next to smallest observations and should have at least moderately high efficiencies. Also, some extensions are considered, such as allowing each observation to be from a different population.     

Simultaneous Confidence Intervals for the Population Cell Means,for Two-by-Two Factorial Data,that Utilize Uncertain Prior Information

Consider a two-by-two factorial experiment with more than one replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist confidence intervals for the four population cell means, with simultaneous confidence coefficient 1 ? α, that utilize this prior information in the following sense. These simultaneous confidence intervals define a cube with expected volume that (a) is relatively small when the two-factor interaction is zero and (b) has maximum value that is not too large. Also, these intervals coincide with the standard simultaneous confidence intervals obtained by Tukey’s method, with simultaneous confidence coefficient 1 ? α, when the data strongly contradict the prior information that the two-factor interaction is zero. We illustrate the application of these new simultaneous confidence intervals to a real data set.     

Constructing quantile confidence intervals using extended simple random sample in finite populations

This paper constructs quantile confidence intervals based on extended simple random sample (SRS) from a finite population, where ranks of population units are all known. Extended simple random sample borrows additional information from unmeasured observations in the population by conditioning on the population ranks of the measured units in SRS. The confidence intervals are improved using Rao-Blackwell theorem over the conditional distribution of sample ranks given the measured sample units. Empirical evidence shows that the proposed confidence intervals have shorter lengths than confidence intervals constructed from an SRS sample.     

Confidence and prediction intervals based on interpolated records

In several statistical problems, nonparametric confidence intervals for population quantiles can be constructed and their coverage probabilities can be computed exactly, but cannot in general be rendered equal to a pre-determined level. The same difficulty arises for coverage probabilities of nonparametric prediction intervals for future observations. One solution to this difficulty is to interpolate between intervals which have the closest coverage probability from above and below to the pre-determined level. In this paper, confidence intervals for population quantiles are constructed based on interpolated upper and lower records. Subsequently, prediction intervals are obtained for future upper records based on interpolated upper records. Additionally, we derive upper bounds for the coverage error of these confidence and prediction intervals. Finally, our results are applied to some real data sets. Also, a comparison via a simulation study is done with similar classical intervals obtained before.     

Empirical likelihood confidence intervals for the mean of a population containing many zero values

If a population contains many zero values and the sample size is not very large, the traditional normal approximation‐based confidence intervals for the population mean may have poor coverage probabilities. This problem is substantially reduced by constructing parametric likelihood ratio intervals when an appropriate mixture model can be found. In the context of survey sampling, however, there is a general preference for making minimal assumptions about the population under study. The authors have therefore investigated the coverage properties of nonparametric empirical likelihood confidence intervals for the population mean. They show that under a variety of hypothetical populations, these intervals often outperformed parametric likelihood intervals by having more balanced coverage rates and larger lower bounds. The authors illustrate their methodology using data from the Canadian Labour Force Survey for the year 2000.     

Nonparametric confidence and tolerance intervals from record values data

In a number of situations only observations that exceed or only those that fall below the current extreme value are recorded. Examples include meteorology, hydrology, athletic events and mining. Industrial stress testing is also an example in which only items that are weaker than all the observed items are destroyed. In this paper, it is shown that, how record values can be used to provide distribution-free confidence intervals for population quantiles and tolerance intervals. We provide some tables that help one choose the appropriate record values and present a numerical example. Also universal upper bounds for the expectation of the length of the confidence intervals are derived. The results may be of interest in situation where only record values are stored.     

Multiple comparisons with a control for exponential location parameters under heteroscedasticity

In this paper, a new design-oriented two-stage two-sided simultaneous confidence intervals, for comparing several exponential populations with control population in terms of location parameters under heteroscedasticity, are proposed. If there is a prior information that the location parameter of k exponential populations are not less than the location parameter of control population, one-sided simultaneous confidence intervals provide more inferential sensitivity than two-sided simultaneous confidence intervals. But the two-sided simultaneous confidence intervals have advantages over the one-sided simultaneous confidence intervals as they provide both lower and upper bounds for the parameters of interest. The proposed design-oriented two-stage two-sided simultaneous confidence intervals provide the benefits of both the two-stage one-sided and two-sided simultaneous confidence intervals. When the additional sample at the second stage may not be available due to the experimental budget shortage or other factors in an experiment, one-stage two-sided confidence intervals are proposed, which combine the advantages of one-stage one-sided and two-sided simultaneous confidence intervals. The critical constants are obtained using the techniques given in Lam [9,10]. These critical constant are compared with the critical constants obtained by Bonferroni inequality techniques and found that critical constant obtained by Lam [9,10] are less conservative than critical constants computed from the Bonferroni inequality technique. Implementation of the proposed simultaneous confidence intervals is demonstrated by a numerical example.     

A GEE approach to estimating accuracy and its confidence intervals for correlated data

In this paper, we provide a method for constructing confidence interval for accuracy in correlated observations, where one sample of patients is being rated by two or more diagnostic tests. Confidence intervals for other measures of diagnostic tests, such as sensitivity, specificity, positive predictive value, and negative predictive value, have already been developed for clustered or correlated observations using the generalized estimating equations (GEE) method. Here, we use the GEE and delta‐method to construct confidence intervals for accuracy, the proportion of patients who are correctly classified. Simulation results verify that the estimated confidence intervals exhibit consistent/appropriate coverage rates.     

Construction of Confidence Intervals for the IVIean of a Population Containing Many Zero Values

The likelihood ratio method is used to construct a confidence interval for a population mean when sampling from a population with certain characteristics found in many applications, such as auditing. Specifically, a sample taken from this type of population usually consists of a very large number of zero values, plus a small number of nonzero values that follow some continuous distribution. In this situation, the traditional confidence interval constructed for the population mean is known to be unreliable. This article derives confidence intervals based on the likelihood-ratio-test approach by assuming (1) a normal distribution (normal algorithm) and (2) an exponential distribution (exponential algorithm). Because the error population distribution is usually unknown, it is important to study the robustness of the proposed procedures. We perform an extensive simulation study to compare the percentage of confidence intervals containing the true population mean using the two proposed algorithms with the percentage obtained from the traditional method based on the central limit theorem. It is shown that the normal algorithm is the most robust procedure against many different distributional error assumptions.