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].     

Modified ratio estimators using robust regression methods

When there is an outlier in the data set, the efficiency of traditional methods decreases. In order to solve this problem, Kadilar et al. (2007) adapted Huber-M method which is only one of robust regression methods to ratio-type estimators and decreased the effect of outlier problem. In this study, new ratio-type estimators are proposed by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods based on the Kadilar et al. (2007). Theoretically, we obtain the mean square error (MSE) for these estimators. We compared with MSE values of proposed estimators and MSE values of estimators based on Huber-M and OLS methods. As a result of these comparisons, we observed that our proposed estimators give more efficient results than both Huber M approach which was proposed by Kadilar et al. (2007) and OLS approach. Also, under all conditions, all of the other proposed estimators except Lad method are more efficient than robust estimators proposed by Kadilar et al. (2007). And, these theoretical results are supported with the aid of a numerical example and simulation by basing on data that includes an outlier.     

Estimation of Population Mean Under Non Response in Two-Occasion Rotation Patterns

The present article is an attempt to study the effect of non response at both occasions in search of good rotation patterns over two occasions. Ratio-type estimators were proposed for estimating the population mean at current occasion in presence of non response at both the occasions in two-occasion successive (rotation) sampling. Detail behaviors of proposed estimators were studied. Proposed estimators were compared with the estimator using no information from previous (first) occasion. Performances of the proposed estimators were demonstrated via empirical studies.     

A new class of ratio-type estimators for improving mean estimation of nonsensitive and sensitive variables by using supplementary information

ABSTRACT

Motivated by some recent improvements for mean estimation in finite sampling theory, we propose, in a design-based approach, a new class of ratio-type estimators. The class is initially discussed on the assumption that the study variable has a nonsensitive nature, meaning that it deals with topics that do not generate embarrassment when respondents are directly questioned about them. Under this standard setting, some estimators belonging to the class are shown and the bias, mean square error and minimum mean square error are determined up to the first-order of approximation. The class is subsequently extended to the case where the study variable refers to sensitive issues which produce measurement errors due to nonresponses and/or untruthful reporting. These errors may be reduced by enhancing respondent cooperation through scrambled response methods that mask the true value of the sensitive variable. Hence, four methods (say the additive, multiplicative, mixed and combined additive-multiplicative methods) are discussed for the purposes of the article. Finally, a simulation study is carried out to assess the performance of the proposed class by comparing a number of competing estimators, both in the sensitive and the nonsensitive setting.     

Estimators for the Population Mean in the Case of Missing Data

We propose a class of estimators for the population mean when there are missing data in the data set. Obtaining the mean square error equations of the proposed estimators, we show the conditions where the proposed estimators are more efficient than the sample mean, ratio-type estimators, and the estimators in Singh and Horn (2000 Singh , S. , Horn , S. ( 2000 ). Compromised imputation in survey sampling . Metrika 51 : 267 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]) and Singh and Deo (2003 Singh , S. , Deo , B. (2003). Imputation by power transformation. Statist. Pap. 44:555–579.[Crossref], [Web of Science ®] , [Google Scholar]) in the case of missing data. These conditions are also supported by a numerical example.