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Multivariate Ratio Estimator of the Population Total under Stratified Random Sampling  [PDF]
Oscar O. Ngesa, G. O. Orwa, R. O. Otieno, H. M. Murray
Open Journal of Statistics (OJS) , 2012, DOI: 10.4236/ojs.2012.23036
Abstract: Olkin [1] proposed a ratio estimator considering p auxiliary variables under simple random sampling. As is expected, Simple Random Sampling comes with relatively low levels of precision especially with regard to the fact that its variance is greatest amongst all the sampling schemes. We extend this to stratified random sampling and we consider a case where the strata have varying weights. We have proposed a Multivariate Ratio Estimator for the population mean in the presence of two auxiliary variables under Stratified Random Sampling with L strata. Based on an empirical study with simulations in R statistical software, the proposed estimator was found to have a smaller bias as compared to Olkin’s estimator.
Dual To Ratio Cum Product Estimator In Stratified Random Sampling  [PDF]
Rajesh Singh,Mukesh Kumar,Manoj K. Chaudhary,Cem Kadilar
Statistics , 2013,
Abstract: Tracy et al.[8] have introduced a family of estimators using Srivenkataramana and Tracy ([6],[7]) transformation in simple random sampling. In this article, we have proposed a dual to ratio-cum-product estimator in stratified random sampling. The expressions of the mean square error of the proposed estimators are derived. Also, the theoretical findings are supported by a numerical example.
Local Polynomial Regression Estimator of the Finite Population Total under Stratified Random Sampling: A Model-Based Approach  [PDF]
Charles K. Syengo, Sarah Pyeye, George O. Orwa, Romanus O. Odhiambo
Open Journal of Statistics (OJS) , 2016, DOI: 10.4236/ojs.2016.66088
Abstract: In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.
Exponential Ratio Type Estimators In Stratified Random Sampling  [PDF]
Rajesh Singh,Mukesh Kumar,R. D. Singh,M. K. Chaudhry
Statistics , 2013,
Abstract: Kadilar and Cingi (2003) have introduced a family of estimators using auxiliary information in stratified random sampling. In this paper, we propose the ratio estimator for the estimation of population mean in the stratified random sampling by using the estimators in Bahl and Tuteja (1991) and Kadilar and Cingi (2003). Obtaining the mean square error (MSE) equations of the proposed estimators, we find theoretical conditions that the proposed estimators are more efficient than the other estimators. These theoretical findings are supported by a numerical example.
An improved estimator for population mean using auxiliary information in stratified random sampling  [PDF]
Sachin Malik,Viplav Kumar Singh,Rajesh Singh
Statistics , 2014,
Abstract: In the present study, we propose a new estimator for population mean of the study variable y in the case of stratified random sampling using the information based on auxiliary variable x. Expression for the mean squared error (MSE) of the proposed estimators is derived up to the first order of approximation. The theoretical conditions have also been verified by a numerical example. An empirical study is carried out to show the efficiency of the suggested estimator over sample mean estimator, usual separate ratio, separate product estimator and other proposed estimators.
IMPROVED EXPONENTIAL ESTIMATOR IN STRATIFIED RANDOM SAMPLING
Rajesh Singh
Pakistan Journal of Statistics and Operation Research , 2010, DOI: 10.1234/pjsor.v5i2.118
Abstract: In this article we have considered the problem of estimating the population mean in the stratified random sampling using the information of an auxiliary variable x which is correlated with y and suggested improved exponential ratio estimators in the stratified random sampling. The mean square error (MSE) equations for the proposed estimators have been derived and it is shown that the proposed estimators under optimum condition performs better than estimators suggested by Singh et al. (2008). Theoretical and empirical findings are encouraging and support the soundness of the proposed estimators for mean estimation.
A New Estimator Using Auxiliary Information in Stratified Adaptive Cluster Sampling  [PDF]
Nipaporn Chutiman, Monchaya Chiangpradit, Sujitta Suraphee
Open Journal of Statistics (OJS) , 2013, DOI: 10.4236/ojs.2013.34032
Abstract: In this paper, we study the estimators of the population mean in stratified adaptive cluster sampling by using the information of the auxiliary variable. Simulations showed that if the variable of interest (y) and the auxiliary variables (x,z) have high positive correlation then the estimate of the mean square error of the ratio estimators is less than the estimate of the mean square error of the product estimator. The estimators which use only one auxiliary variable were better than the estimators which use two auxiliary variables.
Computationally Efficient Nonparametric Importance Sampling  [PDF]
Jan C. Neddermeyer
Statistics , 2008,
Abstract: The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric estimation of the optimal importance sampling distribution (known as nonparametric importance sampling) is a reasonable alternative to parametric approaches.In this article nonparametric variants of both the self-normalized and the unnormalized importance sampling estimator are proposed and investigated. A common critique on nonparametric importance sampling is the increased computational burden compared to parametric methods. We solve this problem to a large degree by utilizing the linear blend frequency polygon estimator instead of a kernel estimator. Mean square error convergence properties are investigated leading to recommendations for the efficient application of nonparametric importance sampling. Particularly, we show that nonparametric importance sampling asymptotically attains optimal importance sampling variance. The efficiency of nonparametric importance sampling algorithms heavily relies on the computational efficiency of the employed nonparametric estimator. The linear blend frequency polygon outperforms kernel estimators in terms of certain criteria such as efficient sampling and evaluation. Furthermore, it is compatible with the inversion method for sample generation. This allows to combine our algorithms with other variance reduction techniques such as stratified sampling. Empirical evidence for the usefulness of the suggested algorithms is obtained by means of three benchmark integration problems. As an application we estimate the distribution of the queue length of a spam filter queueing system based on real data.
A New Estimator For Population Mean Using Two Auxiliary Variables in Stratified random Sampling  [PDF]
Rajesh Singh,Sachin Malik
Statistics , 2014,
Abstract: In this paper, we suggest an estimator using two auxiliary variables in stratified random sampling. The propose estimator has an improvement over mean per unit estimator as well as some other considered estimators. Expressions for bias and MSE of the estimator are derived up to first degree of approximation. Moreover, these theoretical findings are supported by a numerical example with original data. Key words: Study variable, auxiliary variable, stratified random sampling, bias and mean squared error.
Improved estimator of finite population mean using auxiliary attribute in stratified random sampling  [PDF]
Hemant K. Verma,Prayas Sharma,Rajesh Singh
Statistics , 2014,
Abstract: The present study discuss the problem of estimating the finite population mean using auxiliary attribute in stratified random sampling. In this paper taking the advantage of point bi-serial correlation between the study variable and auxiliary attribute, we have improved the estimation of population mean in stratified random sampling. The expressions for Bias and Mean square error have been derived under stratified random sampling. In addition, an empirical study has been carried out to examine the merits of the proposed estimator over the existing estimators.
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