Efficient Class Of Estimators Research Articles

An Efficient Class of Estimators in Stratified Random Sampling with an Application to Real Data

This research article addresses an efficient separate and combined class of estimators for the population mean estimation based on stratified random sampling (StRS). The first order approximated expressions of bias and mean square error of the proposed separate and combined class of estimators are obtained. A comparative study is conducted to determine the efficiency conditions in which the suggested class of estimators outperforms the contemporary estimators. These efficiency conditions are examined through an extensive simulation study by employing a hypothetically drawn symmetrical and asymmetrical populations. The simulation results have shown that the suggested class of estimators is more effective than the other available estimators. In addition, an application of the proposed methods is also presented by examining a real data set.

Assessing the Effect of Nonresponse and Measurement Error Using a Novel Class of Efficient Estimators

The purpose of any statistical analysis is to uncover the trend using real situations and provide an accurate model for future policies. In order to fulfill this aim, it is important to collect and use the data carefully and minimize the possibility of various types of errors. Nonresponse (NR) and measurement error (ME) are the two major types of nonsampling error that occur in almost every survey. We propose an estimator of the population mean and study its efficacy in the combined and separate effects of NR and ME. Some existing estimators are also considered for comparison. A simulation study was performed to see its efficiency numerically.

New efficient class of estimators of population mean using two-phase sampling

New efficient class of estimators of population mean using two-phase sampling

A class of asymptotically efficient estimators based on sample spacings

In this paper, we consider general classes of estimators based on higher-order sample spacings, called the Generalized Spacings Estimators. Such classes of estimators are obtained by minimizing the Csiszár divergence between the empirical and true distributions for various convex functions, include the “maximum spacing estimators” as well as the maximum likelihood estimators (MLEs) as special cases, and are especially useful when the latter do not exist. These results generalize several earlier studies on spacings-based estimation, by utilizing non-overlapping spacings that are of an order which increases with the sample size. These estimators are shown to be consistent as well as asymptotically normal under a fairly general set of regularity conditions. When the step size and the number of spacings grow with the sample size, an asymptotically efficient class of estimators, called the “Minimum Power Divergence Estimators,” are shown to exist. Simulation studies give further support to the performance of these asymptotically efficient estimators in finite samples and compare well relative to the MLEs. Unlike the MLEs, some of these estimators are also shown to be quite robust under heavy contamination.

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

ABSTRACTIn 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, 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.

An Efficient Class of Estimators for the Finite Population Mean in Ranked Set Sampling

In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.

A Family of Estimators for Estimating Population Variance Using Auxiliary Information in Sample Survey

In this article an efficient class of estimators for estimating finite population variance has been proposed using auxiliary information in simple random sampling. The bias and mean squared error of the proposed estimator is obtained up to the first degree of approximation. It has been shown that the proposed estimator is more efficient than usual unbiased estimator, Isaki (J. Am. Stat. Assoc.78:117-123, 1983), Kadilar and Cingi (Appl. Math. & Comput., 173, 1047-1059, 2006) and Upadhyaya and Singh (Vikram Math. J. 19, 14-17, 1999a). To judge the merits of the proposed estimator, we consider one numerical example.

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) class of estimators. The results have been illustrated through an empirical study.

A wide and efficient class of estimators of population variance under sub-sampling scheme

Here, it is assumed that the prior information on the parameters of first auxiliary variable x is not available, but the prior information on the parameters of second auxiliary variable z is available for improving the estimators of parameters of interest. We consider the situation when the auxiliary variable x is directly and highly correlated with both the study variable y and the second auxiliary variable z. In this paper, we propose a class of estimators of population variance S y of a study variable y when the population mean and variance of an auxiliary variable z are known in advance. We compare efficiency of various classes of estimators of S y . It has been shown that the proposed class is wider and more efficient than the two existing classes defined by Jhajj et al. (J Japan Stat Soc 35(2) (2005), 273–286) even though the same prior information about the second auxiliary variable z is used in all the classes. AMS 2000 subject classification: 62 D 05

Threshold ARCH(1) processes: asymptotic inference

This article discusses large sample inference problems for a first-order ARCH(1) process where threshold appears not only in the mean but also in the variance function. Geometric ergodicity of the process is discussed. Least-squares estimators of parameters are derived and relevant limit results are obtained. Also, the uniform local asymptotic normality of the log-likelihood ratio and a class of efficient estimators are briefly discussed. The model is applied to Korean financial time series.

Measurement Error with Accounting Constraints: Point and Interval Estimation for Latent Data with an Application to U.K. Gross Domestic Product

An econometric methodology is proposed for reconciling inaccurate measures of latent data which are subject to accounting constraints. The method deals with the case in which the measurement errors are serially correlated, generalizing previous contributions. A class of efficient estimators are derived for the latent data. Consistent estimators for the weight matrices applied to the observed information based on a linear regression procedure are obtained together with confidence interval estimators for these weight matrices. Approximate confidence intervals are suggested for the latent data themselves together with specification tests for the assumptions underlying the procedure. An application of the proposed method is made to U.K. Gross Domestic Product in constant prices for 1958Q1–1989Q4.