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A SIMULATION STUDY TO COMPARISON SOME BIASED ESTIMATORS
In this article we proposed new estimators namely, Almost Unbiased Jackknifed Generalized Liu Estimator (AUJGLE)and Almost Unbiased Modified Jackknifed Generalized Liu Estimator(AUMJGLE) for Multiple linear regression , it was studied the efficiency of the proposed estimators by simulating experiment and comparing the proposed estimators with some other estimators, such as Generalized Liu estimator(GLE),Jackknifed Generalized Liu estimator (JGLE),Modified Jackknifed Generalized Liu estimator (MJGLE) by using mean square error (MSE). The new estimators gave good results.
Overview of Statistical Estimation Methods
Oxford University Press, 2013
This chapter provides an overview of methods for estimating parameters and standard errors. Because it is impossible to cover all statistical estimation methods in this chapter, we focus on those approaches that are of general interest and are frequently used in social science research. For each estimation method, the properties of the estimator are highlighted under idealized conditions; drawbacks potentially resulting from violations of ideal conditions are also discussed. In addition, the chapter reviews several widely used computational algorithms for calculating parameter estimates.
In many sampling situations, researchers come across variety of data. These data are largely affected by the parent distribution. There are characteristics which some data share based on the parent distribution. These characteristics define their distribution as well as their behavior. The use of auxiliary variable in estimating a study variable has been on the increase. Auxiliary variable has been used in estimating population means as well as variances. The variance is very sensitive to distribution. Thus, estimating the variance using auxiliary variable might lead to some unexpected results. Hence the need to check the effect of the distribution of the performances of some selected classes of variance estimators. Twelve estimators were selected for comparison. Eight distributions were considered using simulation study. The selected distributions are: Normal, Chi-square, Uniform, Gamma, Exponential, Poisson, Geometric and Binomial. A population size of 330 was used while sample size of 30 was considered using simple random sample without replacement. The estimators were compared using Bias, and Mean Square Error. The performances of the estimators vary in some distributions. The gamma and exponential distributions showed wide variability. The performances of the estimators based on Bias is the same as that based on Mean Square Error. The Mean Square Errors were ranked. The best estimator is t 1 followed be t 10 and t 12. The results showed that the estimators are not distribution free.
In this study, the use of taylor series method in the calculation of some means with single auxiliary variable developed in a simple random sampling and mean square error unit ratio estimators having certain properties was investigated. An application was performed in respect thereof. The study population (mass) included 111 secondary schools from 18 districts of Trabzon province. Auxiliary variable (x) was taken as the number of students whereas the main variable (y) was taken as the number of teachers. Sample size was calculated as 45 for unit ratio that has certain features. Afterwards, theoretically proposed mean and units ratio estimators having certain properties were compared numerically. Random sampling was performed using the SPSS 20 program thus giving an equal chance to the units sampled and variability in the population was protected.
On Construction of Modified Class of Estimators for Population Variance using Auxiliary Attribute
Regular Issue, 2020
In this paper, an improved estimator for population variance has been proposed to improvise the log-type estimators proposed by Kumari et al. (2019). The properties of proposed estimators are derived up to the first order of approximation. The proposed estimatorfound to be betterthan the existing estimatorsin the sense of mean squraed error and percent relative efficiency. A numerical study is included to support the use of the suggested classes of estimators.
Improved Estimation of Population Variance Utilizing Known Auxiliary Parameters
Scholars Journal of Physics, Mathematics and Statistics
Even similar things, whether created artificially or naturally, can vary. We should therefore try to estimate this variation. For improved population variance estimate, we propose a Searls ratio type estimator in the current research employing data on the tri-mean and the third quartile of the auxiliary variable. Up to the first-degree approximation, the suggested estimator's bias and mean squared error (MSE) are determined. The characterising scalar's ideal value is discovered, and given this ideal value, the least MSE is discovered. The mean squared errors of the suggested estimator and the competing estimators are contrasted conceptually and experimentally. Given that it has the lowest MSE of the above competing estimators, the recommended estimator has been shown to be the most effective.