Two-step calibration estimation under multiple auxiliary variables in survey sampling

In this paper, we have proposed a class of mixture regression-cum-ratio estimator for estimating population mean by using information on multiple auxiliary variables and attributes simultaneously in single-phase sampling and analyzed the properties of the estimator. An empirical was carried out to compare the performance of the proposed estimator with the existing estimators of finite population mean using simulated population. It was found that the mixture regression-cum-ratio estimator was more efficient than ratio and regression estimators using one auxiliary variable and attribute, ratio and regression estimators using multiple auxiliary variables and attributes and regression-cum-ratio estimators using multiple auxiliary variables and attributes in single-phase sampling for finite population.

Prior work has shown that effective survey nonresponse adjustment variables should be highly correlated with both the propensity to respond to a survey and the survey variables of interest. In practice, propensity models are often used for nonresponse adjustment with multiple auxiliary variables as predictors. These auxiliary variables may be positively or negatively associated with survey participation, they may be correlated with each other, and can have positive or negative relationships with the survey variables. Yet the consequences for nonresponse adjustment of these conditions are not known to survey practitioners. Simulations are used here to examine the effects of multiple auxiliary variables with opposite relationships with survey participation and the survey variables. The results show that bias and mean square error of adjusted respondent means are substantially different when the predictors have relationships of the same directions compared to when they have opposite directions with either propensity or the survey variables. Implications for nonresponse adjustment and responsive designs will be discussed.

In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information due to its usefulness in estimation methods. The current study presents two new estimators for the distribution function of a finite population based on dual auxiliary variables. The new estimators can be used in situations where the researchers face some sort of complex data set. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator. Besides, an empirical study simulation study has also been conducted to analyse the performance of estimators. It is found that the new suggested estimators of the distribution function of a finite population are more accurate than some of the existing estimators.

In this paper, we have proposed three classes of mixture ratio estimators for estimating population mean by using information on auxiliary variables and attributes simultaneously in two-phase sampling under full, partial and no information cases and analyzed the properties of the estimators. A simulated study was carried out to compare the performance of the proposed estimators with the existing estimators of finite population mean. It has been found that the mixture ratio estimator in full information case using multiple auxiliary variables and attributes is more efficient than mean per unit, ratio estimator using one auxiliary variable and one attribute, ratio estimator using multiple auxiliary variable and multiple auxiliary attributes and mixture ratio estimators in both partial and no information case in two-phase sampling. A mixture ratio estimator in partial information case is more efficient than mixture ratio estimators in no information case.

In this paper, we have proposed estimators of finite population mean using generalized Ratio- cum-product estimator for two-Phase sampling using multi-auxiliary variables under full, partial and no information cases and investigated their finite sample properties. An empirical study is given to compare the performance of the proposed estimators with the existing estimators that utilize auxiliary variable(s) for finite population mean. It has been found that the generalized Ra-tio-cum-product estimator in full information case using multiple auxiliary variables is more efficient than mean per unit, ratio and product estimator using one auxiliary variable, ratio and product estimator using multiple auxiliary variable and ratio-cum-product estimators in both partial and no information case in two phase sampling. A generalized Ratio-cum-product estimator in partial information case is more efficient than Generalized Ratio-cum-product estimator in No information case.

The estimation of proportions is a subject which cannot be circumvented in a first survey sampling course. Estimating the proportion of voters in favour of a political party, based on a political opinion survey, is just one concrete example of this procedure. However, another important issue in survey sampling concerns the proper use of auxiliary information, which typically comes from external sources, such as administrative records or past surveys. Very often, an efficient insertion of the auxiliary information available will improve the precision of the estimations of the mean or the total when a regression estimator is used. Conceptually, it is difficult to justify using a regression estimator for estimating proportions. A student might want to know how the estimation of proportions can be improved when auxiliary information is available. In this article, I present estimators for a proportion which use the logistic regression estimator. Based on logistic models, this estimator efficiently facilitates a good modelling of survey data. The paper's second objective is to estimate a proportion using various sampling plans (such as a Bernoulli sampling and stratified designs). In survey sampling, each sample possesses its own probability and for a given unit, the inclusion probability denotes the probability that the sample will contain that particular unit. Bernoulli sampling may have an important pedagogical value, because students often have trouble with the concept of the inclusion probability. Stratified sampling plans may provide more insight and more precision. Some empirical results derived from applying four sampling plans to a real data base show that estimators of proportions may be made more efficient by the proper use of auxiliary information and that choosing a more satisfactory model may give additional precision. The paper also contains computer code written in S-Plus and a number of exercises.

In survey sampling, the use of auxiliary information can greatly improve the precision of estimates of population total and/or means. Calibration estimation has developed into an important field of research in survey sampling where the auxiliary information plays an important role. In this paper, calibration estimator for cluster sampling with equal clusters have been introduced to improve variance estimator with the aid of auxiliary information and proposed the estimator of variance of calibration estimator. Six distances measures, presented the estimator of the variance of calibration approach estimators are introduced and a simulation study has been conducted to compare between the performance of calibration estimators against Horvitz-Thompson estimator using R statistical package.

This article addresses the problem of estimating the population mean of variable y using information from multiple auxiliary variables in adaptive cluster sampling. We define a class of estimators based on p(>1) auxiliary variables x 1 , x 2 , … . . , x p , derive bias and mean squared error expressions up to order n−1, and determine optimal conditions for minimizing mean squared error. Our findings demonstrate that the proposed estimators outperform the multiple linear regression estimator. We also identify several existing estimators as members of this class, including those introduced by Dryver and Chao (2007), Chutiman and Kumphon (2008), Chutiman (2013), Chaudhry (2014), Chaudhry and Hanif (2015), and Yadav et al. (2016). Furthermore, we obtain the correct values of constants “a” and “b” for the Chaudhry and Hanif (2015) estimator, leading to an accurate expression for its minimum mean squared error. To assess the performance of these estimators, we conduct a simulation study.

Some estimators of a finite population mean using auxiliary information

Calibration approach is becoming more important in survey sampling. Calibration estimation helps in improving the estimates of population parameters by making use of auxiliary information. This paper proposes a new calibration estimator for estimating the population mean in the stratified random sampling with a set of new calibration constraints using known coefficient of variation of the auxiliary variable. The result has also been extended to the case of double sampling in stratified sampling. The proposed estimator has been compared with the estimator developed by Tracy et al. (2003) with the help of simulation study on real datasets.

SUMMARY Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalised spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. They allow straightforward extensions to multiple auxiliary variables and to complex designs. Under standard design conditions, the estimators are design consistent and asymptotically normal, and they admit consistent variance estimation using familiar design-based methods. Data-driven penalty selection is considered in the context of unequal probability sampling designs. Simulation experiments show that the estimators are more efficient than parametric regression estimators when the parametric model is incorrectly specified, while being approximately as efficient when the parametric specification is correct. An example using Forest Health Monitoring survey data from the U.S. Forest Service demonstrates the applicability of the methodology in the context of a two-phase survey with multiple auxiliary variables.

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalized spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. Further, they allow straightforward extensions to multiple auxiliary variables and to complex designs. Under standard design conditions, the estimators are design consistent and asymptotically normal, and they admit consistent variance estimation using familiar design-based methods. Data-driven penalty selection is considered in the context of unequal probability sampling designs. Simulation experiments show that the estimators are more efficient than parametric regression estimators when the parametric model is incorrectly specified, while being approximately as efficient when the parametric specification is correct. An example using Forest Health Monitoring survey data from the U.S. Forest Service demonstrates the applicability of the methodology in the context of a two-phase survey with multiple auxiliary variables.

On the estimation of the general parameter

In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information, due to its usefulness in estimation methods. In this article, our main objective is to discover the problem associated with estimation of the finite population distribution function, using the known auxiliary variable, which occurs as the sample distribution function and the rank of the auxiliary variable. A new family of the finite population distribution function estimators is proposed in the stratified sampling scheme. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator, along with the efficiency conditions. Besides theoretical efficiency comparison, an empirical study has also been conducted to analyze the performance of estimators. A simulation study is also performed to observe the efficiency of the proposed estimators. The implementation of the proposed sampling scheme is illustrated by a practical example.

Motivated by a recent work by Kadilar and Cingi (2008), we proposed three regression-type estimators to overcome the problem of missing data for a study variable. The estimators make optimal use of the available auxiliary information. We show that, given the same amount of information, these estimators are simpler and more efficient than those proposed by Kadilar and Cingi. A numerical illustration, performed on three different populations, highlights the efficiency gain from using our proposal. Finally, a suggestion is made regarding the optimal use of auxiliary information in sampling practice.