ASN-minimax double sampling plans for variables

X be a continuous quality characteristic, with one-sided lower specification limit, having either normal distribution with known σ or exponential distribution. We report on an algorithm allowing the calculation of the so-called ASN-Minimax plan. This plan has minimal maximal average sample size among all double sampling plans for variables that obey the classical two-points-condition on the operating characteristic. We give examples and tables of the ASN-Minimax plans in the normal as well as in the exponential case. Received: March 20, 2000; revised version: January 22, 2001     

Ordered Random Fractions For Chronological Sampling

The method was devised for use in reference testing under the Average Quantity System, but appears to be of more general interest. It is useful where a chronological list of sampling points is required, as in sampling over time or from items in a line.     

Approximation of homogeneous random field from local averages

Based on the Shannon sampling theorem of multivariate functions, the upper bound of approximated error of homogeneous random field by local averages in the mean square sense is established. The main result is that the approximation of weak sense stochastic process from local averages is extended to the case of random field. It is expected that one can obtain more precise local average sampling in oceanography, meteorology, geology with this theory.     

The role of acceptance sampling in modern quality control

Acceptance sampling procedures can be employedina program of accept ance control to achievebetterqualityat lowercost. An overview of the application of moder nacceptance samplingplans, schemes, andsys tems is described with emphas is on the iruse in facilitating process control. Sampling procedures must continually bemade to matchexist in gconditions, and to self-destruct whennolonger warranted. In this way they can be usedinane voluti on ary manne rina continuing program of acceptance control for quality improvement. Implemen- tation of process control canbefacilitated by on-going application of acceptance control to achieve the full be nefits of statistical quality control.     

A New Proof of Murthy's Estimator which Applies to Sequential Sampling

Murthy's estimator has been used for constructing an unbiased estimator of a population total or mean from a sample of fixed size when there is unequal probability sampling without replacement. Traditionally, the estimator is derived by constructing an unordered version of Raj's ordered unbiased estimator. This paper presents an elementary proof of Murthy's estimator which applies the Rao–Blackwell theorem to a very simple estimator. This proof includes any sequential sampling scheme, thus extending the usefulness of Murthy's estimator. We demonstrate this extension by deriving unbiased estimators for inverse sampling.     

Remainder modified systematic sampling in the presence of linear trend

If the population size is not a multiple of the sample size, then the usual linear systematic sampling design is unattractive, since the sample size obtained will either vary, or be constant and different to the required sample size. Only a few modified systematic sampling designs are known to deal with this problem and in the presence of linear trend, most of these designs do not provide favorable results. In this paper, a modified systematic sampling design, known as remainder modified systematic sampling (RMSS), is introduced. There are seven cases of RMSS and the results in this paper suggest that the proposed design is favorable, regardless of each case, while providing linear trend-free sampling results for three of the seven cases. To obtain linear trend-free sampling for the other cases and thus improve results, an end corrections estimator is constructed.     

A New Sampling Design for Systematic Sampling

A sampling design called “Modified Systematic Sampling (MSS)” is proposed. In this design each unit has an equal probability of selection. Moreover, it works for both situations: N = nk or N ≠ nk. Consequently, the Linear Systematic Sampling (LSS) and Circular Systematic Sampling (CSS) become special cases of the proposed MSS design.     

Kernel Density Estimator From Ranked Set Samples

We study kernel density estimator from the ranked set samples (RSS). In the kernel density estimator, the selection of the bandwidth gives strong influence on the resulting estimate. In this article, we consider several different choices of the bandwidth and compare their asymptotic mean integrated square errors (MISE). We also propose a plug-in estimator of the bandwidth to minimize the asymptotic MISE. We numerically compare the MISE of the proposed kernel estimator (having the plug-in bandwidth estimator) to its simple random sampling counterpart. We further propose two estimators for a symmetric distribution, and show that they outperform in MISE all other estimators not considering symmetry. We finally apply the methods in this article to analyzing the tree height data from Platt et al. (1988 Platt, W.J., Evans, G.M., Rathbun, S.L. (1988). The population dynamics of long-lived conifer (Pinus plaustris) (1988). Amer. Natrualist 131:491–525.[Crossref], [Web of Science ®] , [Google Scholar]) and Chen et al. (2003 Chen, Z., Bai, Z., Sinha, B.K. (2003). Ranked Set Sampling: Theory and Applications. New York: Springer. [Google Scholar]).     

Some remarks on the traditional way of circular and diagonal circular systematic sampling schemes

ABSTRACT

In this paper, some deficiencies in traditional selection procedure of circular version of systematic sampling schemes are investigated and alternative methods are proposed. We also suggest some rules of thumb for coincidence of units in the sample. The end corrections proposed by Bellhouse and Rao (1975 Bellhouse, D.R., Rao, J.N.K. (1975). Systematic sampling in the presence of a trend. Biometrika. 62:694–697.[Crossref], [Web of Science ®] , [Google Scholar]) and Sampath and Varalakshmi (2008) for circular systematic sampling and diagonal circular systematic sampling, respectively, are also modified.     

不等概率抽取群单位时样本量的间接计算

讨论了应用设计效应间接计算不等概率抽群的单级整群抽样和二阶段抽样方案样本量的问题,其中包括：所论抽样方案设计效应的估计;估计所论总体的方差,并根据精度要求计算简单随机抽取基本抽样单元时所需的样本量;用设计效应将上述样本量换算成所论抽样方案需要的样本量。     

网络调查中的非抽样误差及其预防措施

互联网的迅速发展,给统计调查方法带来了巨大的影响,在互联网的基础之上发展起来的网络调查方法,以其独特的优势,日益受到人们的青睐。本文结合调查误差分析的理论,根据网络自身的特点,分析了网络调查的非抽样误差的来源,并提出了减少误差的方法。     

A joint-adaptive np control chart with multiple dependent state sampling scheme

Although the classical Shewhart np control chart has been widely used to detect an out-of-control status of manufacturing process, it is static and there is lack of responsiveness to slight process changes. In this paper, an adaptive np control chart with a joint sampling strategy combining double sampling (DS) and variable sampling interval (VSI) is developed. The multiple dependent state sampling scheme is adopted to further improve the performance of the control chart. An economical design model to minimize the general cost of using the proposed chart is established and solved by a genetic algorithm. The numerical results show that comparing to traditional static np control chart, the proposed np chart yields better performance in terms of shorter time to signal an out-of-control process and less expected cost per unit of time. Comparisons are made to show the capability of the proposed chart in yielding average reductions of 5.01% and 8.89%, in the cost of the proposed model compared to situations in which either the DSVSI np chart or the traditional np chart is used.     

Protection of privacy in efficient application of randomized response techniques

In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response (RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion, testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976), Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994) among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika 57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants before they agree to use the randomization device. The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported by CSIR Grant No. 21(0539)/02/EMR-II.     

An extension of Horvitz–Thompson estimator used in adaptive cluster sampling to continuous universe

In this paper, an extension of Horvitz–Thompson estimator used in adaptive cluster sampling to continuous universe is developed. Main new results are presented in theorems. The primary notions of discrete population are transferred to continuous population. First and second order inclusion probabilities for networks are delivered. Horvitz–Thompson estimator for adaptive cluster sampling in continuous universe is constructed. The unbiasedness of the estimator is proven. Variance and unbiased variance estimator are delivered. Finally, the theory is illustrated with an example.     

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。     

A stratified Tracy and Osahan's two-stage randomized response model

ABSTRACT

This paper proposes an alternative two-stage stratified randomized response model based on Tracy and Osahan (1999 Tracy, D.S., Osahan, S.S. (1999). An improved randomized response technique. Pak. J. Stat. 15(1):1–6. [Google Scholar]) model that has an optimal allocation and large gain in precision. It is also shown that the proposed model is more efficient than Kim and Warde (2004 Kim, J., Warde, W. (2004). A stratified Warner randomized response model. J. Stat. Plan. Infer. 120:155–165.[Crossref], [Web of Science ®] , [Google Scholar]) and Kim and Elam (2005 Kim, J.M., Elam, M.E. (2005). A two-stage stratified Warner's randomized response model using optimal allocation. Metrika 61:1–7.[Crossref], [Web of Science ®] , [Google Scholar]) stratified randomized response models under the conditions presented in both the cases of completely truthful reporting and that of not completely truthful reporting by the respondents. Numerical illustrations and graphs are also given in support of the present study.     

The probability of degenerate maximum-likelihood estimates with randomly truncated survival data

We study the nonparametric maximum-likelihood estimator of the marginal distribution function in bivariate data with truncated sum (Woodroofe 1985), and calculate the probability that it will assign zero probability to a range of observed values. We show that in a simple artificial model with uniform intensity in both variables the probability may be expressed using recursive formulae, and that large-sample approximations valid under weak regularity conditions show good agreement with as few as 20 observations. In the uniform-intensity model, the probability of degenerate estimates is rather small, being just over 5% with a dataset of 20 observations and falling below 1% with 125 observations. However, in a model of transfusion-associated AIDS in 125 children and adults (Kalbfleisch and Lawless 1989), the probability of degenerate estimates is much larger—about 30% with 20 observations and 3% with the actual 125 observations. This is largely because both the infection and incubation density are increasing over time. Such a pattern makes the condition for degeneracy, i.e., relatively high observed intensity at extreme values of each variable, much more likely.     

On the comparison of Horvitz–Thompson and Murthy's sampling strategies for estimating finite population proportions in direct and randomized response surveys

We consider the problem of unbiased estimation of a finite population proportion and compare the relative efficiency of the unequal probability sampling strategies due to Horvitz and Thompson (1952 Horvitz, D.G., Thompson, D.J. (1952). A generalization of sampling without replacement. J Am Stat Assoc. 47:663–685.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Murthy (1957 Murthy, M.N. (1957). Ordered and unordered estimators in sampling without replacement. Sankhya 18:379–390. [Google Scholar]) under a super-population model. It is shown that the model expected variance is smaller for the Murthy's (1957 Murthy, M.N. (1957). Ordered and unordered estimators in sampling without replacement. Sankhya 18:379–390. [Google Scholar]) strategy both when these two sampling strategies are based on data obtained from (i) a direct survey, and (ii) a randomized response (RR) survey employing some RR technique following a general RR model.     

Combined double sampling and variable sampling interval np chart

A combined double sampling and variable sampling interval (DSVSI) np chart is investigated in this study. The optimal design of the DSVSI np chart is based on minimizing the out-of-control average time to signal. From the numerical results, the DSVSI np chart performs reasonably well in comparison with the standard np chart, double sampling np chart, synthetic double sampling np chart, and other existing np type control charts for detecting increases in the process of fraction non conforming, based on the zero-state case. An example is provided to illustrate the application of the DSVSI np chart.     

An adept-stratified Kuk's randomized response model using Neyman allocation

This paper suggests a new stratified randomized response model based on Kuk's [Biometrika (1990), 77, 2, pp.436–438] model that has Neyman allocation and considerable gain in precision. It has been identified that the stratified randomized response models due to Kim and Warde (2004 Kim, J., Warde, W. (2004). A stratified Warner randomized response model. J. Stat. Plan. Inference 120:155–165.[Crossref], [Web of Science ®] , [Google Scholar]), Kim and Elam's (2005), and Kim and Elam's (2007) are members of the proposed model. It is shown that the proposed model is more efficient than Kuk's (1990) model both theoretically and empirically. The results of this paper are also extended in the situation when trials are repeated.