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.     

Estimation of population mean and variance in flock management: a ranked set sampling approach in a finite population setting

Ranked set sampling is a sampling technique that provides substantial cost efficiency in experiments where a quick, inexpensive ranking procedure is available to rank the units prior to formal, expensive and precise measurements. Although the theoretical properties and relative efficiencies of this approach with respect to simple random sampling have been extensively studied in the literature for the infinite population setting, the use of ranked set sampling methods has not yet been explored widely for finite populations. The purpose of this study is to use sheep population data from the Research Farm at Ataturk University, Erzurum, Turkey, to demonstrate the practical benefits of ranked set sampling procedures relative to the more commonly used simple random sampling estimation of the population mean and variance in a finite population. It is shown that the ranked set sample mean remains unbiased for the population mean as is the case for the infinite population, but the variance estimators are unbiased only with use of the finite population correction factor. Both mean and variance estimators provide substantial improvement over their simple random sample counterparts.     

Estimation of partially specified spatial panel data models with random-effects and spatially correlated error components

This paper studies estimation of a partially specified spatial panel data linear regression with random-effects and spatially correlated error components. Under the assumption of exogenous spatial weighting matrix and exogenous regressors, the unknown parameter is estimated by applying the instrumental variable estimation. Under some sufficient conditions, the proposed estimator for the finite dimensional parameters is shown to be root-N consistent and asymptotically normally distributed; the proposed estimator for the unknown function is shown to be consistent and asymptotically distributed as well, though at a rate slower than root-N. Consistent estimators for the asymptotic variance–covariance matrices of both the parametric and unknown components are provided. The Monte Carlo simulation results suggest that the approach has some practical value.     

Estimation of Population Mean in the Presence of Linear Trend

The present article deals with some methods for estimation of finite populations means in the presence of linear trend among the population values. As a result, we provided a strategy for the selection of sampling interval k for the case of circular systematic sampling, which ensures better estimator for the population mean compared to other choices of the sampling interval. This has been established based on empirical studies. Further we more, applied multiple random starts methods for selecting random samples for the case of linear systematic sampling and diagonal systematic sampling schemes. We also derived the explicit expressions for the variances and their estimates. The relative performances of simple random sampling, linear systematic sampling and diagonal systematic sampling schemes with single and multiple random starts are also assessed based on numerical examples.     

Location-shifts for improved estimation under Midzuno–Sen sampling scheme

Simple location-shifts for the study or auxiliary character are proposed under Midzuno–Sen sampling from a finite population. These aim at improving the efficiency of the classical Horvitz–Thompson estimator or the unbiased ratio estimator of a population total. It is demonstrated that the choice of the translation parameters is flexible. A few methods for assessing these parameters are outlined. The gain in efficiency of estimation is illustrated.     

A Mixed Model-assisted Regression Estimator that Uses Variables Employed at the Design Stage

The Generalized regression estimator (GREG) of a finite population mean or total has been shown to be asymptotically optimal when the working linear regression model upon which it is based includes variables related to the sampling design. In this paper a regression estimator assisted by a linear mixed superpopulation model is proposed. It accounts for the extra information coming from the design in the random component of the model and saves degrees of freedom in finite sample estimation. This procedure combines the larger asymptotic efficiency of the optimal estimator and the greater finite sample stability of the GREG. Design based properties of the proposed estimator are discussed and a small simulation study is conducted to explore its finite sample performance.     

Geostatistical Analysis Through Spectral Techniques: Some Words of Caution

Tapering is a technique proposed in order to avoid the so-called edge-effects in spectral estimation. Recent literature has emphasised the importance of tapering for spectral methods applied to the analysis of spatial dependence. In this work we show, through applications and an extensive simulation study, that tapering can be very dangerous if it is not used with caution. An interesting aspect of spectral estimation arises in the presence of a nugget effect in the spatial structure.     

Spatially correlated Poisson sampling

A new method for sampling from a finite population that is spread in one, two or more dimensions is presented. Weights are used to create strong negative correlations between the inclusion indicators of nearby units. The method can be used to produce unequal probability samples that are well spread over the population in every dimension, without any spatial stratification. Since the method is very general there are numerous possible applications, especially in sampling of natural resources where spatially balanced sampling has proven to be efficient. Two examples show that the method gives better estimates than other commonly used designs.     

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.     

Star-Type Systematic Sampling Schemes for Finite Populations

Two new sampling schemes namely, Star-Type Systematic (STS) sampling without replacement and Modified Star-Type Systematic (MSTS) sampling without replacement for estimation of finite population means are introduced. The relative performances of the proposed star-type systematic sample means along with those of the simple random and systematic sample means are assessed for a hypothetical population with a linear trend and also for certain natural populations. Furthermore, the usefulness of the proposed sampling schemes in quality control and for constructing partial diallel crosses in mating designs are briefly break discussed.     

Spatial dependence estimation using FFT of biased covariances

One of the main problems in geostatistics is fitting a valid variogram or covariogram model in order to describe the underlying dependence structure in the data. The dependence between observations can be also modeled in the spectral domain, but the traditional methods based on the periodogram as an estimator of the spectral density may present some problems for the spatial case. In this work, we propose an estimation method for the covariogram parameters based on the fast Fourier transform (FFT) of biased covariances. The performance of this estimator for finite samples is compared through a simulation study with other classical methods stated in spatial domain, such as weighted least squares and maximum likelihood, as well as with other spectral estimators. Additionally, an example of application to real data is given.     

Two-stage informative cluster sampling—estimation and prediction with applications for small-area models

This paper considers the effects of informative two-stage cluster sampling on estimation and prediction. The aims of this article are twofold: first to estimate the parameters of the superpopulation model for two-stage cluster sampling from a finite population, when the sampling design for both stages is informative, using maximum likelihood estimation methods based on the sample-likelihood function; secondly to predict the finite population total and to predict the cluster-specific effects and the cluster totals for clusters in the sample and for clusters not in the sample. To achieve this we derive the sample and sample-complement distributions and the moments of the first and second stage measurements. Also we derive the conditional sample and conditional sample-complement distributions and the moments of the cluster-specific effects given the cluster measurements. It should be noted that classical design-based inference that consists of weighting the sample observations by the inverse of sample selection probabilities cannot be applied for the prediction of the cluster-specific effects for clusters not in the sample. Also we give an alternative justification of the Royall [1976. The linear least squares prediction approach to two-stage sampling. Journal of the American Statistical Association 71, 657–664] predictor of the finite population total under two-stage cluster population. Furthermore, small-area models are studied under informative sampling.     

Asymptotics for REML estimation of spatial covariance parameters

In agricultural field trials, restricted maximum likelihood estimation (REML) of the spatial covariance parameters is often preferred to maximum likelihood. Although it has either been conjectured or assumed that REML estimators are asymptotically Gaussian, conditions under which such asymptotic results hold are clearly needed. This article gives checkable conditions for spatial regression when sampling locations are either on a rectangular grid or are irregularly spaced but satisfy certain growth conditions.     

A weighted spatial median for clustered data

A weighted spatial median is proposed for the multivariate one-sample location problem with clustered data. Its limiting distribution is derived under mild conditions (no moment assumptions) and it is shown to be multivariate normal. Asymptotic as well as finite sample efficiencies and breakdown properties are considered, and the theoretical results are supplied with illustrative examples. It turns out that there is a potential for meaningful gains in estimation efficiency: the weighted spatial median has superior efficiency to the unweighted spatial median particularly when the cluster sizes are widely disparate and in the presence of strong intracluster correlation. The unweighted spatial median for clustered data was considered earlier by Nevalainen et al. (Can J Statist, in press, 2007). The proposed weighted estimators provide companion estimates to the weighted affine invariant sign test proposed recently by Larocque et al. (Biometrika, in press, 2007). An affine equivariant weighted spatial median is discussed in parallel.     

Use of several auxiliary variables in estimating the population mean in a two-occasion rotation pattern

ABSTRACT

This paper addresses the problem of estimation of the population mean on the current (second) occasion in two-occasion successive sampling. Utilizing the readily available information on several auxiliary variables on both occasions and the information on the study variable from the previous occasion, an estimation procedure of the population mean on the current occasion has been proposed. Theoretical properties of the proposed estimator have been investigated. Optimum replacement policy to the proposed estimator has been discussed. The proposed estimator has been compared empirically with the sample mean estimator, when there is no matching and the optimum estimator which is a linear combination of the means of the matched and unmatched portions of the sample at the current occasion. Appropriate recommendations have been made for practical applications.     

Interval estimators for the population mean for skewed distributions with a small sample size

In finite population sampling, it has long been known that, for small sample sizes, when sampling from a skewed population, the usual frequentist intervals for the population mean cover the true value less often than their stated frequency of coverage. Recently, a non-informative Bayesian approach to some problems in finite population sampling has been developed, which is based on the 'Polya posterior'. For large sample sizes, these methods often closely mimic standard frequentist methods. In this paper, a modification of the 'Polya posterior', which employs the weighted Polya distribution, is shown to give interval estimators with improved coverage properties for problems with skewed populations and small sample sizes. This approach also yields improved tests for hypotheses about the mean of a skewed distribution.     

Generalized Systematic Sampling

In this paper, we introduce a new systematic sampling design, called a Generalized Systematic Sampling (GSS), for estimation of finite population mean. The proposed design is found to be better than Simple Random Sampling (SRS) and the generalization of the several existing systematic sampling schemes such as, Linear Systematic Sampling (LSS), Diagonal Systematic Sampling (DSS), and Generalized Diagonal Systematic Sampling (GDSS). All of these designs become special cases of the proposed design.     

Estimation of population product in presence of non-response in successive sampling

The design of this paper is to examine the problem of estimation of finite population product in mail surveys for the current occasion in the context of sampling on two occasions is attempted when there is non-response on both the occasions. Estimators for the current occasion are derived as a particular case when there is non-response on first and second occasion only. The gain in efficiency of the proposed estimate over the direct estimate using no information gathered on the first occasion is computed. The proposed strategy has been compared with other estimators. An empirical study is carried out to study the performance of the proposed strategy.     

Adjusting the bias of adaptive sampling estimators of spatial dispersion indexes by the δ-method

It is common practice to investigate the spatial dispersion in a community of discrete individuals (like animals or plants). Usually, the study area is partitioned into spatial units of equal size and then the relationship between the first two moments of the variable representing the number of individuals in each plot is investigated. When the points are spread over a very wide area so that the population density is low but many points are concentrated inside a few units, then a suitable sample method for estimating the first two moments is adaptive sampling. However, since the more common dispersion indexes are non linear function of the first two moments, the resulting estimators are biased for finite samples. Accordingly, a procedure to adjust bias is required for small samples. In this paper a δ-method evaluation of the bias is proposed and the asymptotic distribution of the bias-corrected estimators is provided. Finally, a simulation study is performed in order to investigate the performance of the proposed procedure.     

On the Use of Superpopulation Model in Estimation of Population Mean in Two-Occasion Rotation Patterns

The present work is an attempt to study the estimation of the population mean on the current occasion in two-occasion successive (rotation) sampling under a superpopulation model. Six different estimators are proposed for estimating the current population mean in two-occasion successive (rotation) sampling. Optimum replacement policies and performances of the proposed estimators have been discussed. Results are interpreted via empirical studies.