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The crux of the paper is to develop a very general class of estimators for population mean Y¯of the study variable yusing information on auxiliary variable xin simple random sampling. It has been shown that a large number of known and unknown estimators are members of the suggested class of estimators. Expressions of bias and mean squared errors of the proposed class of estimators have been obtained under large sample approximation. Asymptotic optimum estimator (AOE) in the proposed class of estimators has been obtained with its mean squared error formula. An empirical study is carried out to demonstrate the superiority of the members of the proposed class of estimators over existing estimators.

The information on auxiliary variables has been shown to be beneficial to improve the precision of study variable estimates. In this paper, an improved exponential ratio estimator is suggested and verified using auxiliary variable information for population variance under simple random sampling. The proposed estimator's bias and mean squared error (MSE) equation is derived up to first order of approximation. The optimal values of characterizing scalars are obtained and the minimum value of MSE of suggested estimator is also obtained. Using the real data sets and simulation study, the performance assessment of the proposed estimator is considered and compared to the competing estimators. The empirical and simulation findings demonstrate that the suggested estimator outperforms the competing estimators.

This article proposes a class of estimators for estimating the population mean of the study variate and analyzes its properties in post-stratified sampling. A computational study is carried out in order to judge the merits of the suggested estimator over conventional simple mean estimator, usual unbiased estimator in post-stratified sampling and other estimators of this category.

Taking clue from pioneer work of Chen and Singh (J Mod Appl Stat Methods 11:105–122, 2012), we have suggested a generalized RR procedure, for estimating the multinomial proportions of potentially sensitive attributes in survey sampling, using higher order moments of scrambling variables at the estimation stage to produce unbiased estimators. The RR procedure due to Chen and Singh (J Mod Appl Stat Methods 11:105–122, 2012) is viewed as member of the proposed RR procedure. Expressions for variance and covariance of the suggested generalized estimator with its development are derived. It is found that the developed estimator is more efficient than Warner’s (J Am Stat Assoc 60:63–69, 1965) RRT. A numerical illustration is also given in support of the present study.

In this paper, we have suggested a weighted unbiased estimator based on mixed randomized response model. Some unbiased estimators are generated from the proposed weighted estimator. The variance of the proposed weighted estimator is obtained and relevant condition is obtained in which the proposed weighted estimator is superior to Singh and Tarray (Sociol Methods Res 44(4):706–722, 2014) estimator. It is interesting to mention that we have investigated an estimator $$ \hat{\pi }_{{{\text{HS}}\left( 1 \right)}} $$ π^HS1 which is the member of the suggested weighted estimator $$ \hat{\pi }_{\text{HS}} $$ π^HS provide better efficiency than the Singh and Tarray’s (2014) estimator $$ \hat{\pi }_{\text{h}} $$ π^h and close to the optimum estimator $$ \hat{\pi }_{\text{HS}}^{{\left( {\text{o}} \right)}} $$ π^HSo . Thus, the estimator $$ \hat{\pi }_{{{\text{HS}}\left( 1 \right)}} $$ π^HS1 is an alternative to optimum estimator $$ \hat{\pi }_{\text{HS}}^{{\left( {\text{o}} \right)}} $$ π^HSo . The study is further extended in case of stratified random sampling.

This article proposes an efficient stratified randomized response model based on the Mangat et al. model. We have obtained the variance of the proposed estimator of πs, the proportion of the respondents in the population belonging to a sensitive group, under proportional and Neyman allocations. It is shown that the estimator based on the proposed model is more efficient than the Mangat et al. estimator under both proportional as well as Neyman allocations, the Hong et al. estimator, and Kim andWarde’s estimator. We have also examined the superiority of the suggested estimator over the Mangat et al. estimator, the Hong et al. estimator, and Kim and Warde’s estimator with the aid of numerical illustration and pictorial representation.

This paper advocates the problem of estimating the population mean on the current occasion in two occasion successive (rotation) sampling under the transformed auxiliary variable using exponential method of estimation. Four different type estimators are suggested for estimating the current population mean in two occasion successive (rotation) sampling. Optimum replacement policies and performance of suggested estimators have been discussed. Outcomes are interpreted through empirical study.

In this paper we have suggested a generalized version of the Gjestvang and Singh (2006) model and have studied its properties. We have shown that the randomized response models due to Warner (1965), Mangat and Singh (1990), Mangat (1994) and Gjestvang and Singh (2006) are members of the proposed RR model. The conditions are obtained in which the suggested RR model is more efficient than the Warner (1965) model, Mangat and Singh (1990) model and Mangat (1994) model and Gjestvang and Singh (2006) model. A numerical illustration is given in support of the present study.

In this article we have suggested some improved estimators of a scale parameter of log-logistic distribution (LLD) under a situation where the units in a sample can be ordered by judgement method without any error. We have also suggested some linear shrinkage estimator of a scale parameter of LLD. Efficiency comparisons are also made in this work.

This paper presents the problem of estimating the population mean on current occasion in two-occasions successive sampling using multiauxiliary variate at both the occasions. We have presented the comprehensive review of the work based on chain-type estimators using single and multiauxiliary variate(s) at both the occasions. A new chain-type multivariate regression estimator for estimating the population mean on current occasion in two-occasion successive sampling is also suggested. Optimum replacement policy relevant to the proposed estimation procedure has been discussed. It has been shown empirically that the proposed multivariate regression estimator is more efficient than the simple mean estimator when there is no matching, the optimal successive sampling estimator when no additional auxiliary information is used and other estimator based on multiauxiliary variates.

AbstractThis paper addresses the problem of estimating the population variance of the study variable y using information on coefficient of variation Cxof an auxiliary variable x. We have suggested a class of estimators for the population variance. Expressions of bias and mean squared error of the proposed class of estimators are obtained under large sample approximation. It is identified that the usual unbiased estimator and Das and Tripathi’s (1978) estimators are members of the suggested class of estimators. It has been shown that proposed class of estimators is more efficient than usual unbiased estimator and Das and Tripathi’s (1978) estimators. An empirical study is given in support of the present study.

The crux of this article is to recast the estimator due to Koyuncu (Appl Math Comp 218:10900–10905, 2012) for the mean utilizing information on an auxiliary attribute. We have derived the bias and mean squared error of the developed estimator under large sample approximation. The best values of the constants are derived for which the mean squared error of the newly developed estimator is minimum. The region of parameters that are obtained in the envisaged estimator is more precise than Koyuncu (Appl Math Comp 218:10900–10905, 2012) estimator and other competent estimators. This reality has been also examined through an empirical study.

This paper proposes a family of estimators of population variance S2yof the study variable yin the presence of known population variance S2xof the auxiliary variable x. It is identified that in addition to many, the recently proposed classes of estimators due to Sharma and Singh (2014) and Singh and Pal (2016) are members of the proposed family of estimators. Asymptotic expressions of bias and mean squared error (MSE) of the suggested family of estimators have been obtained. Asymptotic optimum estimator (AOE) in the family of estimators is identified. Some subclasses of estimators of the proposed family of estimators have been identified along with their properties. We have also given the theoretical comparisons among the estimators discussed in this paper.

In this paper, we have suggested some classes of shrinkage estimators of scale parameter envisaged by Shy and Chacko (Calcutta Stat Assoc Bull 62:143–158, 2010) based on k-record values using uniform distribution. We have shown the superiority of the proposed estimators over Shy and Chacko (Calcutta Stat Assoc Bull 62:143–158, 2010) estimator.

This article proposed an extended class of regression-cum ratio estimator to estimate the mean of sensitive variable with the occurrence of measurement errors. The article considers the use of scramble variable in RRT techniques to estimate the parameters of the sensitive variable. Mean square error has been computed in the presence of measurement error for proposed estimator as well as members of the estimators. In order to show the efficacy of the proposed class of estimator, simulation study has been conducted. The influence of measurement errors on the mean square errors of the proposed estimator as well as members of the estimator for the different levels of scramble variable is obtained.

In this paper we have suggested an exponential estimator of ratio cum product-type for finite population mean in double sampling for stratification. The proposed estimator's bias and mean squared error were obtained up to the first order of approximation. Comparisons have been made theoretically and numerically both with unbiased estimator, ratio and product-type estimator, ratio and product-type exponential estimators. In support of the work, an empirical study is also performed.

This paper suggests a general class of estimators for unknown general population parameter of the study variable using auxiliary information in sample surveys. A large number of estimators of different parameters of the study variable based on auxiliary information can be viewed as a member of the suggested class of estimators. We have derived the bias and mean squared error of the suggested class of estimators under large sample approximation. Optimum conditions are obtained for which the proposed class of estimator has the minimum mean squared error. In particular, a class of estimators for the population mean of the study variable based on the coefficient variation of the auxiliary variable has been derived. The bias and mean squared error of the proposed class of estimators are obtained under large sample approximation. It has been shown that the proposed class of estimators is better than the usual unbiased estimator y¯and Das and Tripathi’s (Sankhya C 42(1–2):76–86, 1980) estimator in the context of bivariate normal and bivariate non-normal populations. In support of the present study, an empirical is given.

Abstract: Taking the clue from the pioneer work of Land et al. (2011), we have suggested an unbiased estimator of the mean number of persons possessing the rare sensitive attribute in presence of the known proportion of persons possessing a rare unrelated attribute. The variance expression is derived. The empirical studies performed and graphical representation show that the new model is more efficient than the one recently considered by Land et al. (2011). [Copyright &y& Elsevier]

Abstract.This paper considers the problem of estimating the population mean of the study variable Yusing systematic sampling in presence of an auxiliary variable X. A class of estimators is proposed and its properties are studied under large sample approximation. It is shown that the proposed class of estimators is more efficient under certain realistic conditions than the usual unbiased estimator, e.g., Swain's (1964) ratio estimator, Shukla's (1971) product estimator and modified estimators. The two phase sampling version of the suggested class of estimators in systematic sampling is introduced along with its properties. An empirical study is provided to illustrate the results of this paper.

This article addresses the problem of estimating the population mean in systematic sampling using information on an auxiliary variable. A class of estimators for the population mean is defined with its properties under large sample approximation. It has been shown that the proposed class of estimators is better than the usual unbiased estimator, Swain (1964) estimator, Shukla (1971) estimator, and usual regression estimator. The results have been illustrated through an empirical study.

The problem of estimating the finite population mean on the samples selected over two occasions in presence of non-response has been considered. For the case when several auxiliary variables are positively correlated with the study variable, a double sampling multivariate ratio estimate from the matched portion of the sample is presented. Estimators for the current occasion are derived as a particular case when there is non-response on first (second) occasion respectively. The gain in efficiency and the cost function of the combined estimators over the direct estimate using no information gathered on the first occasion is computed. The comparison between the proposed strategy with other estimators is also carried out. An empirical study is also included for illustration.

This paper addresses the problem of estimating the population mean using auxiliary information. Improved versions of Bahl and Tuteja (1991) ratio and product exponential type estimators have been proposed and their properties studied under large sample approximation. It has been shown that the proposed ratio and product exponential type estimators are more efficient than those considered by Bahl and Tuteja (1991) estimators, conventional ratio and product estimators and the usual unbiased estimator under some realistic conditions. An empirical study has been carried out to judge the merits of the suggested estimators over others. Theoretical and empirical results are sound and quite illuminating compared to other estimators.

For estimating the mean, ratio and product we have considered the estimation of general parameter R(a)(= µY0/µY 1(a),µY1? 0) using the information on an auxiliary variable Xwhose population mean µXis assumed to be known, in the presence of measurement errors, where µY0and µY1are the population means of the study variables Y0and Y1respectively; a being a scalar takes values,1 (for population ratio R= µY0/µY1), -1 (for population product P= µY0µY1), and 0 (for population mean µY0). A class of estimators for estimating the general parameter R(a)has been defined and asymptotic expressions for its bias and mean squared error (MSE) have been obtained. A comparative study has been made among the proposed estimators and the conventional estimators Numerical illustration is given in support of the present study.

In this paper we envisaged some improved classes of shrinkage estimators for estimating scale parameter of one parameter exponential distribution, when some apriori or guessed interval containing the parameter θ(say) is available from some past experiences. Simulation study have carried out to verify the high efficiency of the proposed new classes of estimators when compared with the usual consistent estimators, unbiased estimator, minimum mean squared error estimator and Singh and Chander’s estimators.

This paper deals with the problem of estimating the population ratio, product and mean using auxiliary information in two-phase sampling in presence of non-response. Three classes of estimators are proposed along with their properties. Asymptotic optimum estimators (AOEs) have been investigated with their approximate mean squared error formulae. Estimators based on estimated optimum values have also been given. It has been shown that to the first degree of approximation the mean squared errors of the estimators based on estimated optimum values have the mean squared errors equal to the mean squared errors of asymptotic optimum estimators (AOEs). An empirical study is carried to show the performance of the various estimators relative to the conventional estimator.

In this paper we have considered the problem of estimating the variance of the stratified random sample mean using information on a supplementary variate x. Various classes of estimators have been proposed and their properties are studied. It has been shown that the proposed classes of estimators are more efficient than usual unbiased estimator. An empirical study is carried out in support of the present study.

This paper is intended to propose an improved class of shrinkage estimators for estimating the general parameter P(a)= ?a(a, being an integer) of the Inverse Gaussian distribution using prior information ?0aof the parameter P(a)= ?aunder investigation. The properties of the suggested class of shrinkage estimators are studied and compared with the usual unbiased estimator, minimum mean squared error (MMSE) estimator and Singh and Pandit’s (2006) estimator. Realistic condition have been obtained under which the proposed class of shrinkage estimators are better than these estimators. In particular, the study has been concentrated over the problem of estimation of shape parameter P(1) = ?and the measure of dispersion P(-1) =1/?of the Inverse Gaussian distribution. Numerical illustrations are given in the support of the proposed study.

In this paper we have suggested a family of estimators of a density f(y) of a random variable Ybased upon a set of observations taken from a bivariate joint density β(x, y) of Yand a suitably chosen concomitant random variable Xso that f(y) = ∫ β(x, y)dx. It is shown that the estimator envisaged by Ahmad and Singh (1989) is a particular member of the proposed family. Asymptotic expressions for bias and variance of the proposed family are obtained. Asymptotically optimum estimator (AOE) in the class is also identified.

This paper proposes a modified randomization device for collecting information on sensitive issues. The estimator based on the suggested strategy is found to be unbiased for population proportion and is better than the Greenberg et. al.'s (1969) estimator. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper deals with the problem of estimating the components of the variance of one-way random effects model under non-normality situation using a prior knowledge of coefficient of kurtosis. We have suggested two classes of estimators $\hat \sigma _{(p)}^2 $ and $\hat \sigma _{(q)}^2 $ for the within and between variances respectively. Optimum estimators in the classes of $\hat \sigma _{(p)}^2 $ and $\hat \sigma _{(q)}^2 $ are identified with their mean squared errors formulae and compared with that of usual ANOVA unbiased and Shoukri, Tracy and Mian's (1990) estimators. It is found that the proposed estimators are more efficient than the ANOVA unbiased estimators and Shoukri, Tracy and Mian (1990) estimators.

This paper proposes several upper bounds of the variance of the estimator π^(say) suggested by Mangat and Singh (1990) making use of an inverse binomial randomized response (IBRR) procedure.

SYNOPTIC ABSTRACTThis paper proposes a class of estimators for estimating population standard deviation using auxiliary information in sample surveys. The large sample expressions for the bias and variance of the estimators are derived and the minimum variance obtained. An empirical study is carried out to demonstrate the performance of the constructed estimators over usual standard deviation estimator.

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

This paper proposes a class of estimators for estimating ratio and product of two means of a finite population using information on two auxiliary characters. Asymptotic expression to terms of order 0(n-1) for bias and mean square error (MSE) of the proposed class of estimators are derived. Optimum conditions are obtained under which the proposed class of estimators has the minimum MSE. An empirical study is carried out to compare the performance of various estimators of ratio with the conventional estimators.

In this paper we propose a general class of almost unbiased estimators for the ratio and product of population means of two charactess.

A class of estimators for the variance of sample mean is defined and its properties are studied in case of normal population. It is identified that the usual unbiased estimator, Singh, Pandey and Hirano (1973) -type estimator and Lee (1931) estimator are particular members of the proposed class of estimators. It is found that the minimum Mean Squared Error (MSE) of the proposed class of estimators is less than that of other estimators.

In this note an attempt has been made to develop a class of unbiased estimators for an unknown parameter. Several estimators can be shown as a direct result of the proposed class.

Summary: In this paper we have proposed a class of almost unbiased ratio-cumproduct estimators for the finite population mean using jackknife techniques envisaged by Quenouille (1956). An asymptotic expression for the variance of the proposed estimator is derived and the optimum estimator in the class is also identified. The conditions for the proposed estimator to be more efficient than the sample mean and Singh’s (1967) biased estimator are obtained. It is also shown that Singh’s (1987) estimators are particular cases of the proposed class. Two illustrative examples are given to demonstrate the superiority of the proposed estimator.

This paper suggests a class of estimators for estimating the finite population mean ?? of the study variable ?? using known population mean ?? of the auxiliary variable ??. Asymptotic expressions of bias and variance of the suggested class of estimators have been obtained. Asymptotic optimum estimator (AOE) in the class is identified along with its variance formula. It has been shown that the proposed class of estimators is more efficient than usual unbiased, usual ratio, usual product, Bahl and Tuteja (1991), and Kadilar and Cingi (2003) estimators under some realistic conditions. An empirical study is carried out to judge the merits of suggested estimator over other competitors practically.