Improved Estimation of Finite Population Variance Using Auxiliary Information

This article addresses the problem of estimating of finite population variance using auxiliary information in simple random sampling. A ratio-cum-difference type class of estimators for population variance has been suggested with its properties under large sample approximation. It has been shown that the suggested class of estimators is more efficient than usual unbiased, difference, Das and Tripathi (1978 Das , A. K. , Tripathi , T. P. ( 1978 ). Use of auxiliary information in estimating the finite population variance . Sankhya C 40 : 139 – 148 . [Google Scholar]), Isaki (1983 Isaki , C. T. ( 1983 ). Variance estimation using auxiliary information . J. Amer. Statist. Assoc. 78 : 117 – 123 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Singh et al. (1988 Singh , H. P. , Upadhyaya , L. N. , Namjoshi , U. D. ( 1988 ). Estimation of finite population variance . Curr. Sci. 57 : 1331 – 1334 .[Web of Science ®] , [Google Scholar]), Kadilar and Cingi (2006 Kadilar , C. , Cingi , H. ( 2006 ). Ratio estimators for the population variance in simple and stratified random sampling . Appl. Math. Comp. 173 ( 2 ): 1047 – 1059 .[Crossref], [Web of Science ®] , [Google Scholar]), and other estimators/classes of estimators. In addition, we support this theoretical result with the aid of a empirical study.     

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information in Stratified Random Sampling

This article addresses the problem of estimating the population mean in stratified random sampling using the information of an auxiliary variable. A class of estimators for population mean is defined with its properties under large sample approximation. In particular, various classes of estimators are identified as particular member of the suggested class. It has been shown that the proposed class of estimators is better than usual unbiased estimator, usual combined ratio estimator, usual product estimator, usual regression estimator and Koyuncu and Kadilar (2009 Koyuncu, N., Kadilar, C. (2009). Ratio and product estimators in stratified random sampling. J. Statist. Plan. Infere. 139:2552–2558.[Crossref], [Web of Science ®] , [Google Scholar]) class of estimators. The results have been illustrated through an empirical study.     

A Class of Estimators Using Auxiliary Information for Estimating Finite Population Variance in Presence of Measurement Errors

This article addresses the problem of estimating the population variance using auxiliary information in the presence of measurement errors. When the measurement error variance associated with study variable is known, a class of estimators of the population variance using auxiliary information has been proposed. We obtain the bias and mean squared errors of the suggested class of estimators upto the terms of order n ^?1, and also optimum estimators in asymptotic sense of the class with approximate mean squared error formula.     

Estimation of Bowley's Coefficient of Skewness in the Presence of Auxiliary Information

In this paper, we suggest regression-type estimators for estimating the Bowley's coefficient of skewness using auxiliary information. To the first degree of approximation, the bias and mean-squared error expressions of the regression-type estimators are obtained, and the regions under which these estimators are more efficient than the conventional estimator are also determined. Further, a general class of estimators of the Bowley's coefficient of skewness is defined along with its properties. A class of estimators based on estimated optimum values is also defined. It is shown to the first degree of approximations that the variance of the class of estimators based on estimated optimum values is the same as that of the minimum variance of the proposed class of estimators. A simulation study is carried out to demonstrate the performance of the proposed difference estimator over the usual estimator.     

On Some Families of Estimators of Variance of Post-Stratified Sample Mean Using Two Auxiliary Variables

In this article, we propose some families of estimators for finite population variance of post-stratified sample mean using information on two auxiliary variables. The families of estimators are discussed in their optimum cases. The MSE of these estimators are derived to the first order of approximation. The percent relative efficiency of proposed families of estimators has been demonstrated with the numerical illustrations.     

Estimation of Median in Two-Phase Sampling Using Two Auxiliary Variables

In recent years, zero-inflated count data models, such as zero-inflated Poisson (ZIP) models, are widely used as the count data with extra zeros are very common in many practical problems. In order to model the correlated count data which are either clustered or repeated and to assess the effects of continuous covariates or of time scales in a flexible way, a class of semiparametric mixed-effects models for zero-inflated count data is considered. In this article, we propose a fully Bayesian inference for such models based on a data augmentation scheme that reflects both random effects of covariates and mixture of zero-inflated distribution. A computational efficient MCMC method which combines the Gibbs sampler and M-H algorithm is implemented to obtain the estimate of the model parameters. Finally, a simulation study and a real example are used to illustrate the proposed methodologies.     

On Improvement in Variance Estimation Using Auxiliary Information

Kadilar and Cingi (2006 Kadilar , C. , Cingi , H. ( 2006 ). Improvement in variance estimation using auxiliary information . Hacett. J. Math. Statist. 35 ( 1 ): 111 – 115 . [Google Scholar]) have introduced an estimator for the population variance using an auxiliary variable in simple random sampling. We propose a new ratio-type exponential estimator for population variance which is always more efficient than usual ratio and regression estimators suggested by Isaki (1983 Isaki , C. T. ( 1983 ). Variance estimation using auxiliary information . J. Amer. Statist. Assoc. 78 : 117 – 123 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and by Kadilar and Cingi (2006 Kadilar , C. , Cingi , H. ( 2006 ). Improvement in variance estimation using auxiliary information . Hacett. J. Math. Statist. 35 ( 1 ): 111 – 115 . [Google Scholar]). Efficiency comparison is carried out both mathematically and numerically.     

Some Classes of Estimators for the Population Median Using Auxiliary Information

This article considers some classes of estimators of the population median of the study variable using information on an auxiliary variable with their properties under large sample approximation. Asymptotic optimum estimator (AOE) in each class of estimators has been investigated along with the approximate mean square error formulae. It has been shown that the proposed classes of estimators are better than these considered by Gross (1980 Gross , T. S. ( 1980 ). Median estimation in sample surveys. Proc. Surv. Res. Meth. Sect. Amer. Statist. Assoc. 181–184 . [Google Scholar]), Kuk and Mak (1989 Kuk , A. Y. C. , Mak , T. K. ( 1989 ). Median estimation in the presence of auxiliary information . J. Roy. Statist. Soc. Ser. B51 : 261 – 269 . [Google Scholar]), Singh et al. (2003a Singh , H. P. , Singh , S. , Joarder , A. H. ( 2003a ). Estimation of population median when mode of an auxiliary variable is known . J. Statist. Res. 37 ( 1 ): 57 – 63 . [Google Scholar]), and Al and Cingi (2009 Al , S. , Cingi , H. ( 2009 ). New estimators for the population median in simple random sampling. Tenth Islamic Countries Conference on Statistical Sciences, held in New Cairo, Egypt . [Google Scholar]). An empirical study is carried out to judge the merits of the suggested class of estimators over other existing estimators.     

Estimation of Finite Population Mean in Stratified Random Sampling with Two Auxiliary Variables under Double Sampling Design

In this article, a chain ratio-product type exponential estimator is proposed for estimating finite population mean in stratified random sampling with two auxiliary variables under double sampling design. Theoretical and empirical results show that the proposed estimator is more efficient than the existing estimators, i.e., usual stratified random sample mean estimator, Chand (1975) chain ratio estimator, Choudhary and Singh (2012) estimator, chain ratio-product-type estimator, Sahoo et al. (1993) difference type estimator, and Kiregyera (1984) regression-type estimator. Two data sets are used to illustrate the performances of different estimators.     

Estimation of Finite Population Variance Using Scrambled Responses in the Presence of Auxiliary Information

In this article, a new estimator for estimating the finite population variance of a sensitive variable based on scrambled responses collected using a randomization device is introduced. The estimator is then improved by using known auxiliary information. The estimators due to Das and Tripathi (1978: Sankhya) and Isaki (1983: JASA) are shown to be special cases of the proposed estimator. Numerical simulations are performed to study the magnitude of the gain in efficiency when using the estimator with auxiliary information with respect to the estimator based only on the scrambled responses. An idea to extend the present work from SRSWOR design to more complex design is also given.     

A Class of Estimators of Population Variance Using Auxiliary Information in Sample Surveys

This article advocates the problem of estimating the population variance of the study variable using information on certain known parameters of an auxiliary variable. A class of estimators for population variance using information on an auxiliary variable has been defined. In addition to many estimators, usual unbiased estimator, Isaki's (1983), Upadhyaya and Singh's (1999), and Kadilar and Cingi's (2006) estimators are shown as members of the proposed class of estimators. Asymptotic expressions for bias and mean square error of the proposed class of estimators have been obtained. An empirical study has been carried out to judge the performance of the various estimators of population variance generated from the proposed class of estimators over usual unbiased estimator, Isaki's (1983), Upadhyaya and Singh's (1999) and Kadilar and Cingi's (2006) estimators.     

On Optimum Regression Estimator for Population Mean Using Two Auxiliary Variables in Simple Random Sampling

In this paper, a difference-in-regression estimator is proposed by using two auxiliary variables in simple random sampling. Variance of proposed estimator up to the first order of approximation is compared with other competing estimators. Additionally, by taking the known value of one of the population regression coefficients, another version of the proposed estimator is also obtained. The proposed estimator is found optimum in the class of estimators based on two auxiliary variables. A simulation study is carried out in support with theoretical results. If only the means of auxiliary variables are available, another estimator can be obtained for large trivariate normal population.     

An improved estimation in stratified random sampling

ABSTRACT

The article suggests a class of estimators of population mean in stratified random sampling using auxiliary information with its properties. In addition, various known estimators/classes of estimators are identified as members of the suggested class. It has been shown that the suggested class of estimators under optimum condition performs better than the usual unbiased, usual combined ratio, usual combined regression, Kadilar and Cingi (2005 Kadilar, C., Cingi, H. (2005). A new ratio estimator in stratified sampling. Commun. Stat. Theory Methods 34:597–602.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Singh and Vishwakarma (2006 Singh, H.P., Vishwakarma, G.K. (2006). Combined ratio-product estimator of finite population mean in stratified sampling. Metodologia de Encuestas Monografico: Incidencias en el trabjo de Campo 7(1):32–40. [Google Scholar]) estimators and the members belonging to the classes of estimators envisaged by Kadilar and Cingi (2003 Kadilar, C., Cingi, H. (2003). Ratio estimator in stratified sampling. Biomet. J. 45:218–225.[Crossref], [Web of Science ®] , [Google Scholar]), Singh, Tailor et al. (2008 Singh, H.P., Agnihotri, N. (2008). A general procedure of estimating population mean using auxiliary information in sample surveys. Stat. Trans. 9(1):71–87. [Google Scholar]), Singh et al. (2009 Singh, R., Kumar, M., Chaudhary, M.K., Kadilar, C. (2009). Improved exponential estimator in stratified random sampling. Pak. J. Stat. Oper. Res. 5(2):67–82.[Crossref] , [Google Scholar]), Singh and Vishwakarma (2010 Singh, H.P., Vishwakarma, G.K. (2010). A general procedure for estimating the population mean in stratified sampling using auxiliary information. METRON 67(1):47–65.[Crossref] , [Google Scholar]) and Koyuncu and Kadilar (2010) Koyuncu, N., Kadilar, C. (2010). On improvement in estimating population mean in stratified random sampling. J. Appl. Stat. 37(6):999–1013.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar].     

Mean Estimation Under Successive Sampling with Calibration Estimators

The estimation of the finite population mean in successive occasions is investigated with calibration estimators in this article. We propose several estimators based on calibration techniques with arbitrary sampling design in each of the occasions. Asymptotic variance formulaes are derived for the proposed estimators. The properties of these estimators are studied via a simulation study and using natural populations.     

An Improved Class of Estimators for the General Population Parameters Using Auxiliary Information

This article suggests an improved class of estimators for estimating the general population parameter using information on an auxiliary variable. The properties of the suggested class of estimators have been studied under large sample approximation. The general results are then applied to estimate the population coefficient of variation of study variable using auxiliary information. An empirical study is given in support of the theoretical results.     

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 Mode Using Auxiliary Information

In this article, we propose naïve estimator, ratio estimator, and difference estimator of the mode of a study variable by using the known mode of an auxiliary variable. The asymptotic properties of the proposed estimators are studied analytically as well as empirically for different situations. The proper use of auxiliary information is found to result in efficient ratio and difference estimators than the naïve estimator.     

On Estimating the Finite Population Mean Using Two Auxiliary Variables in Two Phase Sampling in the Presence of Non Response

This article considers the problem of estimating the population mean using information on two auxiliary variables in the presence of non response under two-phase sampling. Some improved ratio-in-regression type estimators have been proposed in four different situations of non response along with their properties under large sample approximation. Efficiency comparisons of the proposed estimators with the usual unbiased estimator by Hansen and Hurwitz (1946 Hansen , M. H. , Hurwitz , W. N. ( 1946 ). The problem of non response in sample surveys . J. Amer. Statist. Assoc. 41 : 517 – 529 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), conventional ratio and regression estimators using single auxiliary variable and Singh and Kumar (2010b Singh , H. P. , Kumar , S. ( 2010b ). Improved estimation of population mean under double sampling with sub-sampling the non-respondents . J. Statist. Plann. Infer. 140 ( 9 ): 2536 – 2550 .[Crossref], [Web of Science ®] , [Google Scholar]) estimators using two auxiliary variables have been made. Finally, these theoretical findings are illustrated by a numerical example.     

A Correction Note on Improvement in Variance Estimation Using Auxiliary Information

ABSTRACT

In this paper, the testing problem for homogeneity in the mixture exponential family is considered. The model is irregular in the sense that each interest parameter forms a part of the null hypothesis (sub-null hypothesis) and the null hypothesis is the union of the sub-null hypotheses. The generalized likelihood ratio test does not distinguish between the sub-null hypotheses. The Supplementary Score Test is proposed by combining two orthogonalized score tests obtained corresponding to the two sub-null hypotheses after proper reparameterization. The test is easy to design and performs better than the generalized likelihood ratio test and other alternative tests by numerical comparisons.