A general procedure for estimating the mean using double sampling for stratification and multi-auxiliary information

This paper defines a general procedure for estimating the population mean of the study variate based on double sampling for stratification in presence of multi-auxiliary information. Classes of combined and separate estimators have been suggested and their properties are studied under large sample approximation. A class of unstratified double sampling estimators is also proposed with its properties. Asymptotic optimum estimators in the classes are identified with their approximate variance formulae. Further the proposed classes of estimators are compared with the corresponding class of estimators based on un-stratified double sampling. All findings are encouraging and support the soundness of the proposed procedure for mean estimation.     

Estimation of coefficient of dispersion using auxiliary information

In this note, we consider the problem of estimation of coefficient of dispersion of a study variable by making use of known value of the coefficient of dispersion of an auxiliary variable. We propose ratio and regression-type estimators. We derive expressions of bias and variance of the proposed estimators to the first order of approximation. The relative efficiencies of the ratio and regression-type estimators with respect to the naïve estimator are investigated through a simulation study.     

A control chart using an auxiliary variable and repetitive sampling for monitoring process mean

In this paper, a new control chart is proposed by using an auxiliary variable and repetitive sampling in order to enhance the performance of detecting a shift in process mean. The product-difference type estimator of the mean is plotted on the proposed control chart, which utilizes the information of an auxiliary variable correlated with the main quality variable. The proposed control chart is based on the outer and inner control limits so that repetitive sampling is allowed when the plotted statistic falls between the two limits. The average run length (ARL) of the proposed control chart is evaluated using the Monte Carlo simulation. The proposed control chart is compared with the Riaz M control chart and the results show the outperformance of the proposed control chart in terms of the ARL.     

A new synthetic control chart for monitoring process mean using auxiliary information

ABSTRACT

Quality control charts have been widely recognized as a potentially powerful statistical process monitoring tool in statistical process control because of their superior ability in detecting shifts in the process parameters. Recently, auxiliary-information-based control charts have been proposed and shown to have excellent speed in detecting process shifts than those based without it. In this paper, we design a new synthetic control chart that is based on a statistic that utilizes information from both the study and auxiliary variables. The proposed synthetic chart encompasses the classical synthetic chart. The construction, optimal design, run length profiles, and the performance evaluation of the new chart are discussed in detail. It turns out that the proposed synthetic chart performs uniformly better than the classical synthetic chart when detecting different kinds of shifts in the process mean under both zero-state and steady-state run length performances. Moreover, with reasonable assumptions, the proposed chart also surpasses the exponentially weighted moving average control chart. An application with a simulated data set is also presented to explain the implementation of the proposed control chart.     

Optimal use of two auxiliary variables in double sampling

Double sampling scheme is used when cheap auxiliary variables may be measured to improve the estimation of a finite population parameter. Several estimators for population mean, ratio of means and variance are available, when two dependent samples are drawn. However, there are few proposals for the case of independent samples. In this paper both cases of dependent and independent samples are dealt with. A general approach for estimating a finite population parameter is given, showing that all the proposed estimators are particular cases of the same general class. The minimum variance bound for any estimator in this class is provided (at the first order of approximation). Furthermore, an optimal estimator which reaches this minimum is found.     

Estimation of the mean utilizing prior information

Katti [1] et Mehta et Srinivasan [2] ont considérés le probléme d'estimer la moyenne μ d'une population quand de l'information a priori sur μ est disponible. Dans [1], la supposition est que cette information a priori est sous forme d'un “estimé deviné”. Un estimateur à deux degres de deux échantillons est présenté. Quand à [2], un estimateur “shrinkage” basé sur un seul échantillon et une “valeur à priori” est considéré. En suivant les techniques présentées dans ces deux articles, nous suggérons des estimateurs du paramètre quand les données viennent d'une population Binomiale ou Poisson.     

Estimation of population mean on the most recent occasion under non response in h-occasion successive sampling using several auxiliary variables

In this article, general estimation procedures of population mean on the most recent occasion in the presence of non response on all occasions have been deduced in h-occasion successive sampling. In the estimation procedures, regression type estimators have been suggested with the aid of stable and mutually independent several auxiliary variables which are readily available only on the most recent occasion. To check the efficiency of the proposed estimators, they have been compared with similar estimator in absence of non response. Properties of the suggested estimation procedures have been studied and their empirical studies are carried out to validate the theoretical results. Suitable recommendations have been made.     

Estimation of a population mean with two-way stratification using a systematic allocation scheme

A technique of systematically allocating a sample to the strata formed by double stratification is presented. The method can proportionally allocate the sample along each variable of stratification. If there are R strata and C strata for the first and second variable of stratification respectively, the technique requires that the total sample size be at least as large as max(R, C). An unbiased estimator of the population mean is given and its variance is obtained. The technique is compared with a random allocation procedure given by Bryant, Hartley, and Jessen (1960). Numerical examples are given suggesting when one technique is superior to the other.     

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     

Constructing an unbiased estimator of population mean in finite populations using auxiliary information

The objective of this paper is to construct an unbiased estimator (up to order 0(1/n)) of the population mean of the study variatey which is more efficient than the sample mean of the ‘n’ obsrvedy-values. In particular, the unbiased estimators are discussed for the cases of positive and negative correlations of the study variatey and the auxiliary variatex.     

Optimal CUSUM and adaptive CUSUM charts with auxiliary information for process mean

The CUSUM chart is good enough to detect small-to-moderate shifts in the process parameter(s) as it can be optimally designed to detect a particular shift size. The adaptive CUSUM (ACUSUM) chart provides good detection over a range of shift sizes because of its ability to update the reference parameter using the estimated process shift. In this paper, we propose auxiliary-information-based (AIB) optimal CUSUM (OCUSUM) and ACUSUM charts, named AIB-OCUSUM and AIB-ACUSUM charts, using a difference estimator of the process mean. The performance comparisons between existing and proposed charts are made in terms of the average run length (ARL), extra quadratic loss and integral relative ARL measures. It is found that the AIB-OCUSUM and AIB-ACUSUM charts are more sensitive than the AIB-CUSUM and ACUSUM charts, respectively. Moreover, the AIB-ACUSUM chart surpasses the AIB-OCUSUM chart when detecting a range of mean shift sizes. Illustrative examples are given to support the theory.     

A simulation study: estimation of population mean using two auxiliary variables in stratified random sampling

ABSTRACT

This paper deals with the problem of estimating the finite population mean in stratified random sampling by using two auxiliary variables. This paper proposed a ratio-cum-product exponential type estimator of population mean under different situations: (i) when there is presence of non-response and measurement errors on the study as well as auxiliary variables; (ii) when there is non-response on the study and auxiliary variables but with no measurement error; (iii) when there is complete response on study variable but there is presence of non-response and measurement error on the auxiliary variables and (iv) when there are complete response and measurement error on study as well as auxiliary variables. The expressions of the bias and mean square error of the proposed estimator have been obtained up to the first degree of approximation. The proposed estimator has been compared with usual unbiased estimator, ratio estimator and other existing estimators and the conditions obtained to show the efficacy of the proposed estimator over other considered estimators. Simulation study is carried out to support the theoretical findings.     

Allocation of sample using values of auxiliary characteristic

The optimum allocation given by Neyman (1934) is not normally feasible in practice since the values of the standard deviations of the characteristic under study are not known. In this paper, it is shown how the values of auxiliary characteristic linearly related to the study variable can be used in the allocation of the sample. It is also found that proportional allocation can be more efficient than an approximation to Neyman's allocation by using estimates of standard deviations of the study variable from a previous survey or approximations to them from some variable related to the study variable.     

Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables

We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. The strength of this approach lies in its generality and its ease of implementation. The aim of the paper, therefore, is to provide an alternative sampling algorithm to rejection-based methods and other sampling approaches such as the Metropolis–Hastings algorithm.     

Estimation of finite population mean in stratified sampling using scrambled responses in the presence of measurement errors

This study focuses on the estimation of population mean of a sensitive variable in stratified random sampling based on randomized response technique (RRT) when the observations are contaminated by measurement errors (ME). A generalized estimator of population mean is proposed by using additively scrambled responses for the sensitive variable. The expressions for the bias and mean square error (MSE) of the proposed estimator are derived. The performance of the proposed estimator is evaluated both theoretically and empirically. Results are also applied to a real data set.     

The general class of chain estimators for the ratio of two means using double sampling

A wider class of chain based estimators for the ratio of two means of a finite population has been proposed by using two auxiliary variables. Singh et al.(1994) is a particular case of this class.     

Estimation of the mean quality-adjusted survival using a multistate model for the sojourn times

In clinical trials, it may be of interest taking into account physical and emotional well-being in addition to survival when comparing treatments. Quality-adjusted survival time has the advantage of incorporating information about both survival time and quality-of-life. In this paper, we discuss the estimation of the expected value of the quality-adjusted survival, based on multistate models for the sojourn times in health states. Semiparametric and parametric (with exponential distribution) approaches are considered. A simulation study is presented to evaluate the performance of the proposed estimator and the jackknife resampling method is used to compute bias and variance of the estimator.     

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.