Single Auxiliary Variable Research Articles

Calibration estimator of population mean under stratified two-phase sampling using two auxiliary variables

In the present paper, we have tried to discover a new calibration estimator of the population mean under stratified two-phase sampling design utilizing the information on two auxiliary variables. In order to develop the calibration estimator, we have obtained new optimum stratum weights so that the MSE/Variance of the estimator would be minimized. Moreover, we have compared the efficiency of the proposed calibration estimator with that of the calibration estimator considered under the stratified two-phase sampling scheme using single auxiliary variable. An empirical illustration along with a simulation analysis has also been presented to demonstrate the theoretical results.

Efficient Estimator for Population Mean in Stratified Double Sampling in the Presence of Nonresponse Using One Auxiliary Variable

A modified form of the population mean estimator suggested by Anieting and Enang (2020) in stratified double sampling in the presence of nonresponse using a single auxiliary variable has been proposed. The Mean Squared Error (MSE) and the bias of the proposed estimator have been given using large sample approximation. The empirical study shows that the MSE of the suggested estimator is more efficient than all other existing estimators in the same scheme. Determination of the optimal values of the first and second phases samples has also been done

A MODIFIED RATIO TYPE ESTIMATOR OF FINITE POPULATION MEAN UNDER STRATIFIED RANDOM SAMPLING SCHEME

In This paper a modied ratio-type estimator for nite population mean under stratied random sampling using single auxiliary variable has been proposed. The expression for mean square error and bias of the proposed estimator are derived up to the rst order of approximation. The expression for minimum mean square error of proposed estimator is also obtained. The mean square error the proposed estimator is compared with other existing estimators theoretically and condition are obtained under which proposed estimator performed better. A real life population data set has been considered to compare the efciency of the proposed estimator numerically.

Two- Phase Stratified Sampling Estimator for Population Mean in The Presence of Nonresponse Using Single Auxiliary Variable

In this article, a new estimator for population mean in two-phase stratified sampling in the presence of nonresponse using single auxiliary variable has been proposed. The bias and Mean Squared Error (MSE) of the proposed estimator has been given using large sample approximation. The empirical study shows that the MSE of the proposed estimator is more efficient than existing estimators. The optimum values of first and second phase sample have been determined.

ESTIMATING POPULATION COEFFICIENT OF VARIATION USING A SINGLE AUXILIARY VARIABLE IN SIMPLE RANDOM SAMPLING

Abstract This paper proposes an improved estimation method for the population coefficient of variation, which uses information on a single auxiliary variable. The authors derived the expressions for the mean squared error of the proposed estimators up to the first order of approximation. It was demonstrated that the estimators proposed by the authors are more efficient than the existing ones. The results of the study were validated by both empirical and simulation studies.

OPTIMUM STRATIFICATION FOR TWO STRATIFYING VARIABLES

In this paper, we have taken under considerations two auxiliary variables used as stratification variables and single study variable. For obtaining the optimum strata boundaries, we have solved the non linear equations using dynamic programming that resulted in more efficient results rather than obtained on using single study variable and single auxiliary variable. The proposed method is illustrated by using different distributions followed by stratification variables. KEYWORDS: Concomitant Variables, Dynamic Programming, Multistage Decision Problem MSC: 62D05

Empirical distribution function estimators based on sampling designs in a finite population using single auxiliary variable

ABSTRACT In this paper, we study empirical distribution function (EDF) estimators based on ranked set sampling (RSS). Ranked set samples are constructed by using three different sampling designs which are level-0, level-1 and level-2. These designs are different in terms of their replacement policies. The sample is constructed by sampling with replacement in level-0 sampling design. In level-1 sampling design, the sample is constructed by sampling with replacement of the unmeasured units in each set. Also, we construct the sample without replacement on the entire set in level-2 sampling design. In simulation study, we compare EDF estimators when using sampling designs with EDF estimator when using simple random sampling (SRS) in finite populations having different distribution functions. The effects of both perfect and imperfect ranking on the estimators of the sampling designs are investigated. Relative efficiencies of the EDF estimators are obtained by using their integrated mean squared errors (IMSEs), numerically. For illustrative purposes, these EDF estimators based on sampling designs are applied to a real data set. By using both the simulation data and real data, we show that these EDF estimators have higher efficiencies against EDF based on SRS.

Class of trigonometric transformation estimator

Bahl and Tuteja(1991) have given exponential estimator to estimate population mean. Kumar(2006) suggested exponential type estimator in two phase sampling. This note discusses class of trigonometric type estimator in single and double phase sampling using single auxiliary variable. The bias(B) and mean square error(MSE) is obtained up to first order of approximation. Empirical is given to verify the efficiency of the proposed estimators.

Two phase sampling for estimation of population mean with auxiliary information using exponential type of estimator

Bahl and Tuteja(1991) have given exponential estimator to estimate population mean. Kumar(2006) suggested exponential type estimator in two phase sampling. This note discusses class of dual to exponential estimator in two phase sampling using single auxiliary variable. The bias(B) and mean square error(MSE) is obtained up to first order of approximation. The suggested class of estimators is more efficient than Singh(2007),. Empirical is given to verify the efficiency of the proposed estimators.

Two-step calibration of design weights under two auxiliary variables in sample survey

ABSTRACTCalibration on the available auxiliary variables is widely used to increase the precision of the estimates of parameters. Singh and Sedory [Two-step calibration of design weights in survey sampling. Commun Stat Theory Methods. 2016;45(12):3510–3523.] considered the problem of calibration of design weights under two-step for single auxiliary variable. For a given sample, design weights and calibrated weights are set proportional to each other, in the first step. While, in the second step, the value of proportionality constant is determined on the basis of objectives of individual investigator/user for, for example, to get minimum mean squared error or reduction of bias. In this paper, we have suggested to use two auxiliary variables for two-step calibration of the design weights and compared the results with single auxiliary variable for different sample sizes based on simulated and real-life data set. The simulated and real-life application results show that two-auxiliary variables based two-step calibration estimator outperforms the estimator under single auxiliary variable in terms of minimum mean squared error.

Improved estimators for population coefficient of variation using auxiliary variable

This paper propounds an improved estimation of coefficient of variation utilizing information on a single auxiliary variable. The expressions for mean square errors of the proposed estimators have been derived up to first order of approximation. At one hand, among the proposed estimators, some of the estimators under optimum conditions are more efficient than the usual estimator . On the other hand some proposed estimators under optimum conditions are less efficient than the existing estimators. Further an empirical study has been carried out to support the theoretical results and for that we have considered two natural population data sets.

Generalized variance estimators in adaptive cluster sampling using single auxiliary variable

This study presents generalized variance estimators utilizing the information on single auxiliary variable in adaptive cluster sampling for finite population variance. The expressions for mean square errors and biases for proposed variance estimators are obtained. The result of simulation study presents that the suggested variance estimators for adaptive cluster sampling (ACS) design are most efficient for population variance as compare to Isaki (1983) variance estimator for SRSWOR.

Generalized estimator of population mean by using conventional and non-conventional measures in the presence of measurement errors

ABSTRACTIn survey research, it is assumed that reported response by the individual is correct. However, given the issues of prestige bias, self-respect, respondent's reported data often produces estimated values which are highly deviated from the true values. This causes measurement error (ME) to be present in the sample estimates. In this article, the estimation of population mean in the presence of measurement error using information on a single auxiliary variable is studied. A generalized estimator of population mean is proposed. The class of estimators is obtained by using some conventional and non-conventional measures. Simulation and numerical study is also conducted to assess the performance of estimators in the presence and absence of measurement error.

Use of Auxiliary Variables and Asymptotically Optimum Estimators in Double Sampling

This paper explore the need for exploiting auxiliary variables in sample survey and utilizing asymptotically optimum estimator in double sampling to increase the efficiency of estimators. The study proposed two types of estimators with two auxiliary variables for two phase sampling when there is no information about auxiliary variables at population level. The expressions for the Mean Squared Error (MSE) of the proposed estimators were derived to the first order of approximation. An empirical comparative approach of the minimum variances and percent relative efficiency were adopted to study the efficiency of the proposed and existing estimators. It was established that, the proposed estimators performed more efficiently than the mean per unit estimator and other previous estimators that don’t use auxiliary variable and that are not asymptotically optimum. Also, it was established that estimators that are asymptotically optimum that utilized single auxiliary variable are more efficient than those that are not asymptotically optimum with two auxiliary variables.

An EWMA-Type Control Chart for Monitoring the Process Mean Using Auxiliary Information

Statistical process control (SPC) is an important application of statistics in which the outputs of production processes are monitored. Control charts are an important tool of SPC. A very popular category is the Shewhart's -chart used to monitor the mean of a process characteristic. Two alternatives to the Shewhart's -chart are the cumulative sum and exponentially weighted moving average (EWMA) charts which are designed to detect moderate and small shifts in the process mean. Targeting on small and moderate shifts in the process mean, we propose an EWMA-type control chart which utilizes a single auxiliary variable. The regression estimation technique for the mean is used in defining the control structure of the proposed chart. It is shown that the proposed chart is performing better than its univariate and bivariate competitors which are also designed for detecting small shifts.

Compact modeling of allosteric multisite proteins: application to a cell size checkpoint.

We explore a framework to model the dose response of allosteric multisite phosphorylation proteins using a single auxiliary variable. This reduction can closely replicate the steady state behavior of detailed multisite systems such as the Monod-Wyman-Changeux allosteric model or rule-based models. Optimal ultrasensitivity is obtained when the activation of an allosteric protein by its individual sites is concerted and redundant. The reduction makes this framework useful for modeling and analyzing biochemical systems in practical applications, where several multisite proteins may interact simultaneously. As an application we analyze a newly discovered checkpoint signaling pathway in budding yeast, which has been proposed to measure cell growth by monitoring signals generated at sites of plasma membrane growth. We show that the known components of this pathway can form a robust hysteretic switch. In particular, this system incorporates a signal proportional to bud growth or size, a mechanism to read the signal, and an all-or-none response triggered only when the signal reaches a threshold indicating that sufficient growth has occurred.

A New Cost Effective Estimator in the Presence of Non-response for Two-phase Sampling

In In this paper we have proposed a new estimator of population mean in the presence of non–response using information of a single auxiliary variable. We have obtained survey cost for the fixed variance of the proposed estimator and compared it with the cost obtained by Tabasum and Khan (2004) and Hansen Hurwitz (1946). After the comparison we saw that the cost of our proposed estimator is lesser than Tabasum and Khan (2004) and Hansen Hurwitz (1946) estimators.

Stratification of Skewed Populations: A review

Summary When Dalenius provided a set of equations for the determination of stratum boundaries of a single auxiliary variable, that minimise the variance of the Horvitz–Thompson estimator of the mean or total under Neyman allocation for a fixed sample size, he pointed out that, though mathematically correct, those equations are troublesome to solve. Since then there has been a proliferation of approximations of an iterative nature, or otherwise cumbersome, tendered for this problem; many of these approximations assume a uniform distribution within strata, and, in the case of skewed populations, that all strata have the same relative variation. What seems to have been missed is that the combination of these two assumptions offers a much simpler and equally effective method of subdivision for skewed populations; take the stratum boundaries in geometric progression.

Ratio and Product Type Exponential Estimators

Abstract This paper proposes new ratio and product type estimators for estimating the mean of the finite population using information on single auxiliary variable. The bias and mean square error of these estimators have been obtained. These estimators are compared for their precision with usual mean per unit, ratio and product estimators and are found to be more efficient in many practical situations. Further, it is shown that these estimators reduce to regression estimator.