Generalized estimator for the estimation of rare and clustered population variance in adaptive cluster sampling

Adaptive cluster sampling (ACS) is considered to be the most suitable sampling design for the estimation of rare, hidden, clustered and hard-to-reach population units. The main characteristic of this design is that it may select more meaningful samples and provide more efficient estimates for the field investigator as compare to the other conventional sampling designs. In this paper, we proposed a generalized estimator with a single auxiliary variable for the estimation of rare, hidden and highly clustered population variance under ACS design. The expressions of approximate bias and mean square error are derived and the efficiency comparisons have been made with other existing estimators. A numerical study is carried out on a real population of aquatic birds together with an artificial population generated by Poisson cluster process. Related results of numerical study show that the proposed generalized variance estimator is able to provide considerably better results over the competing estimators.     

Rare and clustered population estimation using the adaptive cluster sampling with some robust measures

The use of robust measures helps to increase the precision of the estimators, especially for the estimation of extremely skewed distributions. In this article, a generalized ratio estimator is proposed by using some robust measures with single auxiliary variable under the adaptive cluster sampling (ACS) design. We have incorporated tri-mean (TM), mid-range (MR) and Hodges-Lehman (HL) of the auxiliary variable as robust measures together with some conventional measures. The expressions of bias and mean square error (MSE) of the proposed generalized ratio estimator are derived. Two types of numerical study have been conducted using artificial clustered population and real data application to examine the performance of the proposed estimator over the usual mean per unit estimator under simple random sampling (SRS). Related results of the simulation study show that the proposed estimators provide better estimation results on both real and artificial population over the competing estimators.     

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.     

Variance estimation in adaptive cluster sampling

Abstract

In this paper, a class of variance estimator is proposed of a finite population variance under an adaptive cluster sampling design in the presence of information on an auxiliary variable. We obtain expressions for the mean square error and bias for the developed estimators and their performance is evaluated on a Poisson clustered process and a real data set. The simulation study evaluates the efficiency of the suggested estimators for an adaptive cluster sampling (ACS) design and the Isaki (1983 Isaki, C. T. 1983. Variance estimation using auxiliary information. Journal of the American Statistical Association 78 (381):117–23. doi: 10.1080/01621459.1983.10477939.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) estimator of the variance for SRSWOR over the sample variance for SRSWOR.     

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.     

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.     

Estimation of finite population variance in successive sampling using multi-auxiliary variables

ABSTRACT

In this paper, a general class of estimators for estimating the finite population variance in successive sampling on two occasions using multi-auxiliary variables has been proposed. The expression of variance has also been derived. Further, it has been shown that the proposed general class of estimators is more efficient than the usual variance estimator and the class of variance estimators proposed by Singh et al. (2011) when we used more than one auxiliary variable. In addition, we support this with the aid of numerical illustration.     

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.     

Generalized ratio-type and ratio-exponential-type estimators for population mean under modified Horvitz-Thompson estimator in adaptive cluster sampling

In the present article, we propose the generalized ratio-type and generalized ratio-exponential-type estimators for population mean in adaptive cluster sampling (ACS) under modified Horvitz-Thompson estimator. The proposed estimators utilize the auxiliary information in combination of conventional measures (coefficient of skewness, coefficient of variation, correlation coefficient, covariance, coefficient of kurtosis) and robust measures (tri-mean, Hodges-Lehmann, mid-range) to increase the efficiency of the estimators. Properties of the proposed estimators are discussed using the first order of approximation. The simulation study is conducted to evaluate the performances of the estimators. The results reveal that the proposed estimators are more efficient than competing estimators for population mean in ACS under both modified Hansen-Hurwitz and Horvitz-Thompson estimators.     

Estimation of mean and variance of stigmatized quantitative variable using distinct units in randomized response sampling

Received: April 6, 1998; revised version: July 12, 1999     

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.     

Conditional inference in finite population sampling under a calibration model

Several estimators, including the classical and the regression estimators of finite population mean, are compared, both theoretically and empirically, under a calibration model, where the dependent variable(y), and not the independent variable(x), can be observed for all units of the finite population. It is shown asymptotically that when conditioned on x, the bias of the classical estimator may be much smaller than that of the regression estimators; whereas when conditioned on y, the regression estimator may have much smaller conditional bias than the classical estimator. Since all the y's(not x's) can be observed, it seems appropriate to make comparison under the conditional distribution of each estimator with y fixed. In this case, the regression estimator has smaller variance, smaller conditional bias, and the conditional coverage probability closer to its nominal level     

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.     

Systematic and nonrandom sampling in the presence of polynomial trends

In the case of finite populations with low-order polynomial trends present, the use of the least squares regression estimator of the mean is discussed. A sampling scheme, which optimizes the efficiency of the regression estimator over a particular class of schemes, is presented.     

Ratio- and difference-type estimators for estimating finite population variance

We consider the problem of estimating finite population variance of a study character when information on an auxiliary character is available. We define ratio- and difference-type estimators and obtain the mean-squared error of them approximately. Using a numerical study, we compare the performances of the proposed estimators with some existing variance estimators.     

Calibrated linear unbiased estimators in finite population sampling

Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38] and Rao [2002. Discussion of “Exact linear unbiased estimation in survey sampling”. J. Stat. Plann. Inf. 102, 39–40] suggested some useful techniques of deriving a linear unbiased estimator of a finite population total by modifying a given linear estimator. In this paper we suggest various generalizations of their results. In particular, we search for estimators satisfying the calibration property with respect to a related auxiliary variable and obtain some new calibrated unbiased ratio-type estimators for arbitrary sampling designs. We also explore a few properties of one of the estimators suggested in Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38].     

A generalized improvement procedure for variance bounds for minimum variance unbiased estimator in inverse sampling

New bounds are obtained for the variance of the minimum variance unbiased estimator of p i n inverse sampling. A generalized procedure for further improving the bounds is also discussed.     

Estimation of a finite population total in two-stage and stratified sampling under superpopulation models

Optimal sampling strategies which minimise the expected mean square error for a linear design as well as model-design unbiased estimators for a finite population total for two-stage and stratified sampling are obtained under different superpopu1ation models     

Second-order variance estimation in poststratified two-stage sampling

The linearization or Taylor series variance estimator and jackknife linearization variance estimator are popular for poststratified point estimators. In this note we propose a simple second-order linearization variance estimator for the poststratified estimator of the population total in two-stage sampling, using the second-order Taylor series expansion. We investigate the properties of the proposed variance estimator and its modified version and their empirical performance through some simulation studies in comparison to the standard and jackknife linearization variance estimators. Simulation studies are carried out on both artificially generated data and real data.     

Systematic and nonrandom sampling in the presence of linear trends

In the case of a finite population with a linear trend, improvements in estimation procedures are suggested for several well-known systematic samplingschemes. The use of the least squares regression estimator is examined and a sampling scheme which reduces its expected mean squared error is proposed.