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.     

Two-stage adaptive cluster sampling

Adaptive cluster sampling is usually applied when estimating the abundance of elusive, clustered biological populations. It is commonly supposed that all individuals in the selected area units are detected by the observer, but in many acutal situations this assumption may be highly unrealistic and some individuals may be missed. This paper deals with the problem of handling imperfect detectability in adaptive cluster sampling by using a pure design-based approach. A two-stage adaptive procedure is proposed where the abundance in the selected units is estimated by replicated counts.     

Unbiased estimators for restricted adaptive cluster sampling

In adaptive cluster sampling the size of the final sample is random, thus creating design problems. To get round this, Brown (1994) and Brown & Manly (1998) proposed a modification of the method, placing a restriction on the size of the sample, and using standard but biased estimators for estimating the population mean. But in this paper a new unbiased estimator and an unbiased variance estimator are proposed, based on estimators proposed by Murthy (1957) and extended to sequential and adaptive sampling designs by Salehi & Seber (2001). The paper also considers a restricted version of the adaptive scheme of Salehi & Seber (1997a) in which the networks are selected without replacement, and obtains unbiased estimators. The method is demonstrated by a simple example. Using simulation from this example, the new estimators are shown to compare very favourably with the standard biased estimators.     

Inverse Adaptive Cluster Sampling with Unequal Selection Probabilities: Case Studies on Crab Holes and Arsenic Pollution

Adaptive cluster sampling is an efficient method of estimating the parameters of rare and clustered populations. The method mimics how biologists would like to collect data in the field by targeting survey effort to localised areas where the rare population occurs. Another popular sampling design is inverse sampling. Inverse sampling was developed so as to be able to obtain a sample of rare events having a predetermined size. Ideally, in inverse sampling, the resultant sample set will be sufficiently large to ensure reliable estimation of population parameters. In an effort to combine the good properties of these two designs, adaptive cluster sampling and inverse sampling, we introduce inverse adaptive cluster sampling with unequal selection probabilities. We develop an unbiased estimator of the population total that is applicable to data obtained from such designs. We also develop numerical approximations to this estimator. The efficiency of the estimators that we introduce is investigated through simulation studies based on two real populations: crabs in Al Khor, Qatar and arsenic pollution in Kurdistan, Iran. The simulation results show that our estimators are efficient.     

A general inverse sampling scheme and its application to adaptive cluster sampling

Not having a variance estimator is a seriously weak point of a sampling design from a practical perspective. This paper provides unbiased variance estimators for several sampling designs based on inverse sampling, both with and without an adaptive component. It proposes a new design, which is called the general inverse sampling design, that avoids sampling an infeasibly large number of units. The paper provide estimators for this design as well as its adaptive modification. A simple artificial example is used to demonstrate the computations. The adaptive and non‐adaptive designs are compared using simulations based on real data sets. The results indicate that, for appropriate populations, the adaptive version can have a substantial variance reduction compared with the non‐adaptive version. Also, adaptive general inverse sampling with a limitation on the initial sample size has a greater variance reduction than without the limitation.     

Mass imputation for two-phase sampling

Two-phase sampling is a cost-effective method of data collection using outcome-dependent sampling for the second-phase sample. In order to make efficient use of auxiliary information and to improve domain estimation, mass imputation can be used in two-phase sampling. Rao and Sitter (1995) introduce mass imputation for two-phase sampling and its variance estimation under simple random sampling in both phases. In this paper, we extend the Rao–Sitter method to general sampling design. The proposed method is further extended to mass imputation for categorical data. A limited simulation study is performed to examine the performance of the proposed methods.     

Variance estimation of DEE and regression estimator when a first-phase cluster sample is restratified

We consider a variance estimation when a stratified single stage cluster sample is selected in the first phase and a stratified simple random element sample is selected in the second phase. We propose explicit formulas of (asymptotically), we propose explicit formulas of (asymptotically) unbiased variance estimators for the double expansion estimator and regression estimator. We perform a small simulation study to investigate the performance of the proposed variance estimators. In our simulation study, the proposed variance estimator showed better or comparable performance to the Jackknife variance estimator. We also extend the results to a two-phase sampling design in which a stratified pps with replacement cluster sample is selected in the first phase.     

Estimation of population mean in presence of random non response in two-stage cluster sampling

The present investigation addresses the problem of estimating a finite population mean in two-phase cluster sampling in presence of random non response situations. Utilizing information on an auxiliary variable, regression type estimators has been proposed. Effective imputation techniques have been suggested to deal with the random non response situations. The properties of the proposed estimation strategies have been studied for different cases of random non response situations in practical surveys. The superiority of the suggested methodology over the natural sample mean estimator of population mean has been established through empirical studies carried over the data sets of natural population and artificially generated population.     

Adaptive sampling without replacement of clusters

In a common form of adaptive cluster sampling, an initial sample of units is selected by random sampling without replacement and, whenever the observed value of the unit is sufficiently high, its neighboring units are added to the sample, with the process of adding neighbors repeated if any of the added units are also high valued. In this way, an initial selection of a high-valued unit results in the addition of the entire network of surrounding high-valued units and some low-valued “edge” units where sampling stops. Repeat selections can occur when more than one initially selected unit is in the same network or when an edge unit is shared by more than one added network. Adaptive sampling without replacement of networks avoids some of this repeat selection by sequentially selecting initial sample units only from the part of the population not already in any selected network. The design proposed in this paper carries this step further by selecting initial units only from the population, exclusive of any previously selected networks or edge units.     

Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys

It is well known that two-phase (or double) sampling is of significant use in practice when the population parameter(s) (say, population mean X¯) of the auxiliary variate x is not known. Keeping this in view, we have suggested a class of ratio-product estimators in two-phase sampling with its properties. The asymptotically optimum estimators (AOEs) in the class are identified in two different cases with their variances. Conditions for the proposed estimator to be more efficient than the two-phase sampling ratio, product and mean per unit estimator are investigated. Comparison with single phase sampling is also discussed. An empirical study is carried out to demonstrate the efficiency of the suggested estimator over conventional estimators.     

Estimation of rare and clustered population variance in adaptive cluster sampling

Abstract

Many researchers used auxiliary information together with survey variable to improve the efficiency of population parameters like mean, variance, total and proportion. Ratio and regression estimation are the most commonly used methods that utilized auxiliary information in different ways to get the maximum benefits in the form of high precision of the estimators. Thompson first introduced the concept of Adaptive cluster sampling, which is an appropriate technique for collecting the samples from rare and clustered populations. In this article, a generalized exponential type estimator is proposed and its properties have been studied for the estimation of rare and highly clustered population variance using single auxiliary information. A numerical study is carried out on a real and artificial population to judge the performance of the proposed estimator over the competing estimators. It is shown that the proposed generalized exponential type estimator is more efficient than the adaptive and non adaptive estimators under conventional sampling design.     

Two-Stage Cluster Sampling with Ranked Set Sampling in the Secondary Sampling Frame

Motivated by a real-life problem, we develop a Two-Stage Cluster Sampling with Ranked Set Sampling (TSCRSS) design in the second stage for which we derive an unbiased estimator of population mean and its variance. An unbiased estimator of the variance of mean estimator is also derived. It is proved that the TSCRSS is more efficient—in the sense of having smaller variance—than the conventional two-stage cluster simple random sampling in which the second-stage sampling is with replacement. Using a simulation study on a real-life population, we show that the TSCRSS is more efficient than the conventional two-stage cluster sampling when simple random sampling without replacement is used in both stages.     

One-cluster sampling designs for an autocorrelated population

The variance of the sampling distribution of the sample mean is derived for two sampling designs in which a single cluster is randomly drawn from an autocorrelated population. The derivations are motivated by potential applications to statistical quality control, where a "one-cluster" sampling design may often be used because of ease of implementation, and where it is likely that process output is autocorrelated Scenarios in statistical process control for which either non-overlapping or overlapping clusters are appropriate are described The sampling design variance under non-overlapping clusters is related to the sampling design variance under overlapping clusters through the use of a circular population.     

Adaptive web sampling in ecology

Adaptive sampling strategies for ecological and environmental studies are described in this paper. The motivations for adaptive sampling are discussed. Developments in this area over recent decades are reviewed. Adaptive cluster sampling and a number of its variations are described. The newer class of adaptive web sampling designs and their spatial sampling uses are discussed. Case studies in the use of adaptive sampling strategies with ecological populations are cited. The nature of optimal sampling strategies is described. Design-based and model-based approaches to inference with adaptive sampling strategies are summarized.     

Confidence Intervals for the Median of a Finite Population Based on the Sign Test

This article presents methods for constructing confidence intervals for the median of a finite population under simple random sampling without replacement, stratified random sampling, and cluster sampling. The confidence intervals, as well as point estimates and test statistics, are derived from sign estimating functions which are based on the well-known sign test. Therefore, a unified approach for inference about the median of a finite population is given.     

Improved unbiased estimators in adaptive cluster sampling

Summary.  The usual design-unbiased estimators in adaptive cluster sampling are easy to compute but are not functions of the minimal sufficient statistic and hence can be improved. Improved unbiased estimators obtained by conditioning on sufficient statistics—not necessarily minimal—are described. First, estimators that are as easy to compute as the usual design-unbiased estimators are given. Estimators obtained by conditioning on the minimal sufficient statistic which are more difficult to compute are also discussed. Estimators are compared in examples.     

Hypothesis Testing in Two-Stage Cluster Sampling

Correlated observations often arise in complex sampling schemes such as two-stage cluster sampling. The resulting observations from this sampling scheme usually exhibit certain positive intracluster correlation, as a result of which the standard statistical procedures for testing hypotheses concerning linear combinations of the parameters may lack some of the optimal properties that these possess when the data are uncorrelated. The aim of this paper is to present exact methods for testing these hypotheses by combining within and between cluster information much as in Zhou & Mathew (1993).     

The Calibration for Two-Phase Randomized Response Estimator

This article presents the calibration procedure of the two-phase randomized response (RR) technique for surveying the sensitive characteristic. When the sampling scheme is two-phase or double sampling, auxiliary information known from the entire population can be used, but the auxiliary information should be information available from both the first and second phases of the sample. If there is auxiliary information available from both the first and second phases, then we can improve the ordinary two-phase RR estimator by incorporating this information in the estimation procedure. In this article, we used the new two-step Newton's method for computing unknown constants in the calibration procedure and compared the efficiency of the proposed estimator through some numerical study.     

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。     

Cluster designs to assess the prevalence of acute malnutrition by lot quality assurance sampling: a validation study by computer simulation

Summary.  Traditional lot quality assurance sampling (LQAS) methods require simple random sampling to guarantee valid results. However, cluster sampling has been proposed to reduce the number of random starting points. This study uses simulations to examine the classification error of two such designs, a 67×3 (67 clusters of three observations) and a 33×6 (33 clusters of six observations) sampling scheme to assess the prevalence of global acute malnutrition (GAM). Further, we explore the use of a 67×3 sequential sampling scheme for LQAS classification of GAM prevalence. Results indicate that, for independent clusters with moderate intracluster correlation for the GAM outcome, the three sampling designs maintain approximate validity for LQAS analysis. Sequential sampling can substantially reduce the average sample size that is required for data collection. The presence of intercluster correlation can impact dramatically the classification error that is associated with LQAS analysis.