Recursive computation of inclusion probabilities in ranked-set sampling

We derive recursive algorithms for computing first-order and second-order inclusion probabilities for ranked-set sampling from a finite population. These algorithms make it practical to compute inclusion probabilities even for relatively large sample and population sizes. As an application, we use the inclusion probabilities to examine the performance of Horvitz-Thompson estimators under different varieties of balanced ranked-set sampling. We find that it is only for balanced Level 2 sampling that the Horvitz-Thompson estimator can be relied upon to outperform the simple random sampling mean estimator.     

复杂抽样推断方法体系的比较研究

对复杂样本进行推断通常有两种体系,一种是传统的基于随机化理论的统计推断,另一种是基于模型的统计推断。传统的抽样理论以随机化理论为基础,将总体取值视为固定,随机性仅体现在样本的选取上,对总体的推断依赖于抽样设计。该方法在大样本情况下具有稳健估计量,但在小样本、数据缺失等情况下失效。基于模型的抽样推断认为总体是超总体模型中抽取的一个随机样本,对总体的推断取决于模型的建立,但在不可忽略抽样设计下估计量是有偏估计。在对这两类推断方法分析的基础上,提出抽样设计辅助的模型推断,并指出该方法在复杂抽样中具有重要的应用价值。     

即时计算机辅助会话语言性别差异研究的新方法

即时计算机辅助会话正极大地改变着人类语言生活的面貌,对其中语言性别差异的研究有利于理解计算机辅助会话影响人类语言的范围和机制,也为重新认识现有语言性别差异理论提供重要依据。但现有研究还存在抽样随机性不足、数据分析方法不当等问题,严重地影响了研究结论的信度。鉴于此,有必要在研究中引入新方法,在保证抽样随机性的基础上,根据数据测量类型和变量性质采用卡方检验来推断某一语言变量性别差异的显著性,重新全面审视现有研究的结论。     

Gibbs抽样条件下瓦格纳法则的中国有效性研究

 本文在Gibbs抽样条件下,利用我国1952-2006年经济增长和财政支出的时间序列数据,对瓦格纳法则在中国有效性问题进行了实证检验,并具体考察了中国政府公共支出规模扩张与经济增长之间的平滑变参数特征。实证结果表明中国经济增长与政府公共支出增长之间的因果关系并不确定,两者在数量上的关系具有明显的阶段性特点,其参数在具体形态上呈平滑变参数特征。     

On the existence and uniqueness of the NPMLE in biased sampling models

Identifiability, existence and uniqueness of the non-parametric maximum likelihood estimator (NPMLE) in biased sampling models are thoroughly investigated. The conditions for existence and uniqueness are considered from a different perspective and proofs are simplified. An extension to semi-parametric models is provided.     

A two-phase sampling strategy for large-scale forest carbon budgets

The estimation of forest carbon sources and sinks is an important issue in forest inventories. For monitoring forest carbon budgets, a two-phase strategy is proposed. In the first phase, N points are thrown onto the study region by means of unaligned systematic sampling and then classified as forest or non-forest on the basis of aerial information. In the second phase, a sample of n points of those classified as forest is achieved by means of a sampling scheme with selection probabilities proportional to the sizes of an auxiliary variable. Subsequently, circular plots of adequate size are centred in the n selected points and visited in order to quantify the carbon amount within. Unbiased estimators of the forest area size as well as of the overall amount of carbon in that area and a conservative estimator of their variance–covariance matrix are derived. The strategy is applied to estimate carbon budgets in the forests of Trentino (North Italy).     

Designing of a variables two-plan system by minimizing the average sample number

This article proposes a variables two-plan sampling system called tightened-normal-tightened (TNT) sampling inspection scheme where the quality characteristic follows a normal distribution or a lognormal distribution and has an upper or a lower specification limit. The TNT variables sampling inspection scheme will be useful when testing is costly and destructive. The advantages of the variables TNT scheme over variables single and double sampling plans and attributes TNT scheme are discussed. Tables are also constructed for the selection of parameters of known and unknown standard deviation variables TNT schemes for a given acceptable quality level (AQL) and limiting quality level (LQL). The problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at AQL and LQL under the operating characteristic curve.     

Estimation under systematic sampling schemes for parabolic populations

In this paper, three sampling-estimating strategies involving linear, balanced and modified systematic sampling are considered for the estimation of a finite population total in the presence of parabolic trend. Using appropriate super-population models, their performances are evaluated. For super-population models with constant variance, Yates corrected estimator under linear systematic sampling is shown to perform well. Choices of variance functions under which modified and balanced systematic sampling perform well are also identified based on extensive numerical studies.     

On the Fisher–Bingham distribution

This paper primarily is concerned with the sampling of the Fisher–Bingham distribution and we describe a slice sampling algorithm for doing this. A by-product of this task gave us an infinite mixture representation of the Fisher–Bingham distribution; the mixing distributions being based on the Dirichlet distribution. Finite numerical approximations are considered and a sampling algorithm based on a finite mixture approximation is compared with the slice sampling algorithm.     

Statistical considerations in bioequivalence of two area under the concentration–time curves obtained from serial sampling data

In this paper, we study the bioequivalence (BE) inference problem motivated by pharmacokinetic data that were collected using the serial sampling technique. In serial sampling designs, subjects are independently assigned to one of the two drugs; each subject can be sampled only once, and data are collected at K distinct timepoints from multiple subjects. We consider design and hypothesis testing for the parameter of interest: the area under the concentration–time curve (AUC). Decision rules in demonstrating BE were established using an equivalence test for either the ratio or logarithmic difference of two AUCs. The proposed t-test can deal with cases where two AUCs have unequal variances. To control for the type I error rate, the involved degrees-of-freedom were adjusted using Satterthwaite's approximation. A power formula was derived to allow the determination of necessary sample sizes. Simulation results show that, when the two AUCs have unequal variances, the type I error rate is better controlled by the proposed method compared with a method that only handles equal variances. We also propose an unequal subject allocation method that improves the power relative to that of the equal and symmetric allocation. The methods are illustrated using practical examples.