On huntseerger type shrinkage estimator

This paper is concerned with Hintsberger type weighted shrinkage estimator of a parameter when a target value of the same is available. Expressions for the bias and the mean squared error of the estimator are derived. Some results concerning the bias, existence of uniformly minimum mean squared error estimator etc. are proved. For certain c to ices of the weight function, numerical results are presented for the pretest type weighted shrinkage estimator of the mean of normal as well as exponential distributions.     

Ratio-Cum-Product Type Exponential Estimator of Finite Population Mean in Stratified Random Sampling

This article addresses the problem of estimating the finite population mean in stratified random sampling using auxiliary information. Motivated by Singh (1967 Singh , M. P. ( 1967 ). Ratio cum product method of estimation . Metrika 12 : 34 – 42 .[Crossref] , [Google Scholar]) and Bahl and Tuteja (1991 Bahl , S. , Tuteja , R. K. ( 1991 ). Ratio and product type exponential estimator . Inform. Optimiz. Sci. 12 ( 1 ): 159 – 163 .[Taylor &; Francis Online] , [Google Scholar]) a ratio-cum-product type exponential estimator has been suggested and its bias and mean squared error have been derived under large sample approximation. Suggested estimator has been compared with usual unbiased estimator of population mean in stratified random sampling, combined ratio estimator, combined product estimator, ratio and product type exponential estimator of Singh et al. (2008 Singh , R. , Kumar , M. , Singh , R. D. , Chaudhary , M. K. ( 2008 ). Exponential ratio type estimators in stratified random sampling. Presented in International Symposium on Optimisation and Statistics (I.S.O.S) at A.M.U., Aligarh, India, during 29–31 Dec . [Google Scholar]). Conditions under which suggested estimator is more efficient than other considered estimators have been obtained. A numerical illustration is given in support of the theoretical findings.     

A study on the chain ratio-ratio-type exponential estimator for finite population variance

This paper considers the problem of estimating the population variance S²_y of the study variable y using the auxiliary information in sample surveys. We have suggested the (i) chain ratio-type estimator (on the lines of Kadilar and Cingi (2003)), (ii) chain ratio-ratio-type exponential estimator and their generalized version [on the lines of Singh and Pal (2015)] and studied their properties under large sample approximation. Conditions are obtained under which the proposed estimators are more efficient than usual unbiased estimator s²_y and Isaki (1893) ratio estimator. Improved version of the suggested class of estimators is also given along with its properties. An empirical study is carried out in support of the present study.     

On shrinkage estimation of the exponential location parameter

Under the assumption that the exponential distribution is a reasonable model for a given population, some shrinkage estimators for the location parameter based on type 1 and type II censored samples have been derived. It is shown that these estimators dominate maximum likelihood estimators (MLE's) asymptotically under the mean squared error (MSE) criterion. A Monte Carlo study shows a significant improvement of our estimators over MLE's in terms of MSE for small samples.     

Efficient separate class of estimators of population mean in stratified random sampling

In this paper, efficient class of estimators for population mean using two auxiliary variates is suggested. It has been shown that the suggested estimator is more efficient than usual unbiased estimator in stratified random sampling, usual ratio and product-type estimators, Tailor and Lone (2012 Tailor, R. and Lone, H. A. (2012). Separate ratio-cum- product estimators of finite population mean using auxiliary information. J. Rajasthan Stat. Assoc. 1(2):94–102. [Google Scholar], 2014) estimators, and other considered estimators. The bias and mean-squared error of the suggested estimator are obtained up to the first degree of approximation. Conditions under which the suggested estimator is more efficient than other considered estimators are obtained. An empirical study has been carried out to demonstrate the performances of the suggested estimator.     

On improvement in estimating population mean in stratified random sampling

Gupta and Shabbir 2 Gupta, S. and Shabbir, J. 2008. On improvement in estimating the population mean in simple random sampling. J. Appl. Stat., 35(5): 559–566. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] have suggested an alternative form of ratio-type estimators for estimating the population mean. In this paper, we obtained a corrected version for the mean square error (MSE) of the Gupta–Shabbir estimator, up to first order of approximation, and the optimum case is discussed. We expand this estimator to the stratified random sampling and propose general classes for combined and separate estimators. Also an empirical study is carried out to show the properties of the proposed estimators.     

On generalized exponential chain ratio estimators under stratified two-phase random sampling

Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541–547.[Crossref], [Web of Science ®] , [Google Scholar]) have suggested generalized exponential chain ratio estimators under stratified two-phase sampling scheme for estimating the finite population mean. However, the bias and mean square error (MSE) expressions presented in that work need some corrections, and consequently the study based on efficiency comparison also requires corrections. In this article, we revisit Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541–547.[Crossref], [Web of Science ®] , [Google Scholar]) estimator and provide the correct bias and MSE expressions of their estimator. We also propose an estimator which is more efficient than several competing estimators including the classes of estimators in Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541–547.[Crossref], [Web of Science ®] , [Google Scholar]). Three real datasets are used for efficiency comparisons.     

Ratio and product estimators in stratified random sampling

Khoshnevisan et al. [2007. A general family of estimators for estimating population mean using known value of some population parameter(s). Far East Journal of Theoretical Statistics 22, 181–191] have introduced a family of estimators using auxiliary information in simple random sampling. They have showed that these estimators are more efficient than the classical ratio estimator and that the minimum value of the mean square error (MSE) of this family is equal to the value of MSE of regression estimator. In this article, we adapt the estimators in this family to the stratified random sampling and motivated by the estimator in Searls [1964. Utilization of known coefficient of kurtosis in the estimation procedure of variance. Journal of the American Statistical Association 59, 1225–1226], we also propose a new family of estimators for the stratified random sampling. The expressions of bias and MSE of the adapted and proposed families are derived in a general form. Besides, considering the minimum cases of these MSE equations, the efficient conditions between the adapted and proposed families are obtained. Moreover, these theoretical findings are supported by a numerical example with original data.     

A generalized class of estimators under two-phase stratified sampling for non response

In this paper, we propose a generalized class of estimators for finite population mean using two auxiliary variables in two-phase stratified sampling for non response. We identify 17 estimators as special cases of the proposed class of estimators. Expressions for the bias and mean squared error (MSE) of estimators are obtained up to first order of approximation. A data set is used for efficiency comparisons.     

A new stochastic mixed Liu estimator in linear regression model

Abstract

To overcome multicollinearity, a new stochastic mixed Liu estimator is presented and its efficiency is considered. We also compare the proposed estimators in the sense of matrix mean squared error criteria. Finally a numerical example and a simulation study are given to show the performance of the estimators.     

PMSE dominance of the positive-part shrinkage estimator in a regression model with proxy variables

Consider a linear regression model with some relevant regressors are unobservable. In such a situation, we estimate the model by using the proxy variables as regressors or by simply omitting the relevant regressors. In this paper, we derive the explicit formula of predictive mean squared error (PMSE) of a general family of shrinkage estimators of regression coefficients. It is shown analytically that the positive-part shrinkage estimator dominates the ordinary shrinkage estimator even when proxy variables are used in place of the unobserved variables. Also, as an example, our result is applied to the double k-class estimator proposed by Ullah and Ullah (Double k-class estimators of coefficients in linear regression. Econometrica. 1978;46:705–722). Our numerical results show that the positive-part double k-class estimator with proxy variables has preferable PMSE performance.     

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].     

Estimation of finite population mean in simple and stratified random sampling using two auxiliary variables

We propose an improved difference-cum-exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling using two auxiliary variables. We obtain properties of the estimators up to first order of approximation. The proposed class of estimators is found to be more efficient than the usual sample mean estimator, ratio estimator, exponential ratio type estimator, usual two difference type estimators, Rao (1991) estimator, Gupta and Shabbir (2008) estimator, and Grover and Kaur (2011) estimator. We use six real data sets in simple random sampling and two in stratified sampling for numerical comparisons.     

A new nonparametric estimator for the mean of the selected population

A modified bootstrap estimator of the mean of the population selected from two populations is proposed which is a convex combination of the two sample means, where the weights are random quantities. The estimator is shown to be strongly consistent. The small sample behavior of the estimator is investigated and compared with some competitors by means of Monte Carlo studies. It is found that the newly proposed estimator has smaller mean squared error for a wide range of parameter values.     

A note on a modified double stage shrinkage estimator

A modified double stage shrinkage estimator has been proposed for the single parameter θ of a distribution function _Fθ. It is shown to be locally better in comparison to the usual double stage shrinkage estimator in the sense of smaller mean squared error in a certain neighbourhood of prior estimate θ_o of θ.     

Efficient estimators for adaptive stratified sequential sampling

In stratified sampling, methods for the allocation of effort among strata usually rely on some measure of within-stratum variance. If we do not have enough information about these variances, adaptive allocation can be used. In adaptive allocation designs, surveys are conducted in two phases. Information from the first phase is used to allocate the remaining units among the strata in the second phase. Brown et al. [Adaptive two-stage sequential sampling, Popul. Ecol. 50 (2008), pp. 239–245] introduced an adaptive allocation sampling design – where the final sample size was random – and an unbiased estimator. Here, we derive an unbiased variance estimator for the design, and consider a related design where the final sample size is fixed. Having a fixed final sample size can make survey-planning easier. We introduce a biased Horvitz–Thompson type estimator and a biased sample mean type estimator for the sampling designs. We conduct two simulation studies on honey producers in Kurdistan and synthetic zirconium distribution in a region on the moon. Results show that the introduced estimators are more efficient than the available estimators for both variable and fixed sample size designs, and the conventional unbiased estimator of stratified simple random sampling design. In order to evaluate efficiencies of the introduced designs and their estimator furthermore, we first review some well-known adaptive allocation designs and compare their estimator with the introduced estimators. Simulation results show that the introduced estimators are more efficient than available estimators of these well-known adaptive allocation designs.     

On the predictive performance of the almost unbiased Liu estimator

ABSTRACT

Regression models are usually used in forecasting (predicting) unknown values of the response variable y. This article considers the predictive performance of the almost unbiased Liu estimator compared to the ordinary least-squares estimator, principal component regression estimator, and Liu estimator. Finally, we present a numerical example to explain the theoretical results and we obtain a region where the almost unbiased Liu estimator is uniformly superior to the ordinary least-squares estimator, principal component regression estimator, and Liu estimator.     

An adaptive allocation sampling design for which the conventional stratified estimator is an appropriate estimator

Adaptive allocations in stratified sampling design are suitable for studying Biological and Environmental populations. Biologists tend to use the conventional stratified estimator for an adaptive allocation sampling design in spite of its adaptive nature. In this paper, we have introduced an adaptive allocation sampling design for which the conventional stratified estimator has some desired statistical properties. We conduct a simulation study on a real population. The results show that the conventional stratified estimator for the introduced adaptive allocation sampling design is more efficient than other available estimators.     

Mixed Liu estimator in linear measurement error models

In this paper, we introduce mixed Liu estimator (MLE) for the vector of parameters in linear measurement error models by unifying the sample and the prior information. The MLE is a generalization of the mixed estimator (ME) and Liu estimator (LE). In particular, asymptotic normality properties of the estimators are discussed, and the performance of the MLE over the LE and ME are compared based on mean squared error matrix (MSEM). Finally, a Monte Carlo simulation and a numerical example are also presented for analysis.     

A sufficient condition for the MSE dominance of the positive-part shrinkage estimator when each individual regression coefficient is estimated in a misspecified linear regression model

In this paper, assuming that there exist omitted explanatory variables in the specified model, we derive the exact formula for the mean squared error (MSE) of a general family of shrinkage estimators for each individual regression coefficient. It is shown analytically that when our concern is to estimate each individual regression coefficient, the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators under some conditions even when the relevant regressors are omitted. Also, by numerical evaluations, we showed the effects of our theorem for several specific cases. It is shown that the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators for wide region of parameter space even when there exist omitted variables in the specified model.