Estimating the Population Coefficient of Variation by Confidence Intervals

Several researchers considered various interval estimators for estimating the population coefficient of variation (CV) of symmetric and skewed distributions. Since they considered at different times and under different simulation conditions, their performances are not comparable as a whole. In this article, an attempt has been made to review some existing estimators along with some proposed methods and compare them under the same simulation condition. In particular, we have considered Hendricks and Robey, Mckay, Miller, Sharma and Krishna, Curto and Pinto, and also some bootstrap proposed interval estimators for estimating the population CV. A simulation study has been conducted to compare the performance of the estimators. Both average widths and coverage probabilities are considered as a criterion of the good estimators. Two real life health related data sets are analyzed to illustrate the findings of the article. Based on the simulation study, some possible good interval estimators have been recommended for the practitioners.     

Estimation of Population Mean Using Known Coefficient of Variation of the Study Character in the Presence of Non Response

Using the known coefficient of variation of the study character, generalized and regression-type estimators for the population mean using two phase sampling in the presence of non response were proposed and their properties have been studied. The conditions under which the proposed estimators are more efficient than the relevant estimators have been obtained. The empirical studies were given in the support of the problems in the case of positive and negative correlation between the study and the auxiliary characters which show the increase in the efficiency of the proposed estimators using known coefficient of variation of the study character with respect to the relevant estimators.     

A composite class of estimators using scrambled response mechanism for sensitive population mean in successive sampling

This paper considers the problem of estimation of population mean of a sensitive characteristics using non-sensitive auxiliary variable at current move in two move successive sampling. The proposed estimator is studied under five different scrambled response models. Various estimators have been elaborated to be the member of the proposed class of estimators. The properties of the proposed estimators have been analysed. Many estimators belonging to the proposed class have been explored under five scrambled response models. In order to identify the scrambled model effect, the proposed composite class of estimators is compared to the direct methods. Respondents privacy protection have also been elaborated under different models. Theoretical results are supplemented with numerical demonstrations using real data. Simulation has been carried out to show the applicability of proposed estimators and hence suitable recommendations are forwarded.     

Classes of estimators for population mean using auxiliary variable in stratified population in the presence of non response

In this article, we have proposed six classes of estimators for population mean using auxiliary variable in stratified population with known population mean in the presence of non response on the study variable. The properties of the proposed class of estimators have been studied for fixed sample size. An empirical study has been given in the support of the proposed classes of the estimator.     

A general class of chain estimators for ratio and product of two means of a finite population

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.     

Improved estimation of quantiles of two normal populations with common mean and ordered variances

Abstract

Estimation of quantiles from two normal populations is considered under the assumption of common mean and ordered variances. Several new estimators have been proposed using certain estimators of the common mean, including the plug-in type restricted MLE. A sufficient condition for improving equivariant estimators is proved and as a result improved estimators are derived. The percentage of risk improvements for each of the improved estimators have been computed numerically, which are quite significant. All the improved estimators have been compared numerically using Monte-Carlo simulation method. Finally, recommendations have been made for the use of estimators in practice.     

Bayes Estimator of Inverse Gaussian Parameters Under General Entropy Loss Function Using Lindley's Approximation

In this article, we obtained Bayes estimators of parameters of Inverse Gaussian distributions under asymmetric loss function using Lindley's Approximation (L-Approximation). The proposed estimators have been compared with the corresponding estimators obtained under symmetric loss function and MLE for their risks. This comparison is illustrated using Monte-Carlo study of 2,000 simulated sample from the Inverse Gaussian distribution.     

Confidence intervals for estimating the population signal-to-noise ratio: a simulation study

This paper considered several confidence intervals for estimating the population signal-to-noise ratio based on parametric, non-parametric and modified methods. A simulation study has been conducted to compare the performance of the interval estimators under both symmetric and skewed distributions. We reported coverage probability and average width of the interval estimators. Based on the simulation study, we observed that some of our proposed interval estimators are performing better in the sense of smaller width and coverage probability and have been recommended for the researchers.     

Improvement over variance estimation using auxiliary information in sample surveys

This paper addresses the problem of estimating the population variance S²_y of the study variable y using auxiliary information in sample surveys. We have suggested a class of estimators of the population variance S²_y of the study variable y when the population variance S²_x of the auxiliary variable x is known. Asymptotic expressions of bias and mean squared error (MSE) of the proposed class of estimators have been obtained. Asymptotic optimum estimators in the proposed class of estimators have also been identified along with its MSE formula. A comparison has been provided. We have further provided the double sampling version of the proposed class of estimators. The properties of the double sampling version have been provided under large sample approximation. In addition, we support the present study with aid of a numerical illustration.     

Use of scrambled response model in estimating the finite population mean in presence of non response when coefficient of variation is known

We propose an estimator for the finite population mean utilizing known coefficient of variation of the study character in case of quantitative sensitive variable considering a randomization mechanism on the second call that provides privacy protection to the respondents to get truthful information. We also propose generalized ratio- and regression-type estimators under two-phase sampling scheme. The conditions under which the proposed estimators are more efficient than the relevant estimators under scrambled response model have been obtained. An empirical study is carried out to evaluate performances of the estimators.     

A Generalized Class of Ratio Type Exponential Estimators of Population Mean Under Linear Transformation of Auxiliary Variable

Recently, Shabbir and Gupta [Shabbir, J. and Gupta, S. (2011). On estimating finite population mean in simple and stratified random sampling. Communications in Statistics-Theory and Methods, 40(2), 199–212] defined a class of ratio type exponential estimators of population mean under a very specific linear transformation of auxiliary variable. In the present article, we propose a generalized class of ratio type exponential estimators of population mean in simple random sampling under a very general linear transformation of auxiliary variable. Shabbir and Gupta's [Shabbir, J. and Gupta, S. (2011). On estimating finite population mean in simple and stratified random sampling. Communications in Statistics-Theory and Methods, 40(2), 199–212] class of estimators is a particular member of our proposed class of estimators. It has been found that the optimal estimator of our proposed generalized class of estimators is always more efficient than almost all the existing estimators defined under the same situations. Moreover, in comparison to a few existing estimators, our proposed estimator becomes more efficient under some simple conditions. Theoretical results obtained in the article have been verified by taking a numerical illustration. Finally, a simulation study has been carried out to see the relative performance of our proposed estimator with respect to some existing estimators which are less efficient under certain conditions as compared to the proposed estimator.     

Estimating ordered quantiles of two exponential populations with a common minimum guarantee time

The problem of estimating ordered quantiles of two exponential populations is considered, assuming equality of location parameters (minimum guarantee times), using the quadratic loss function. Under order restrictions, we propose new estimators which are the isotonized version of the MLEs, call it, restricted MLE. A sufficient condition for improving equivariant estimators is derived under order restrictions on the quantiles. Consequently, estimators improving upon the old estimators have been derived. A detailed numerical study has been done to evaluate the performance of proposed estimators using the Monte-Carlo simulation method and recommendations have been made for the use of the estimators.     

A family of efficient estimators of the finite population mean in simple random sampling

In this paper an estimator of the finite population mean using auxiliary information in sample surveys has been proposed. The bias and mean squared error are obtained under large sample approximation. It has been shown that the proposed estimator performs better than some recently published estimators.     

On estimation of the exponentiated Pareto distribution under different sample schemes

Bayes and classical estimators have been obtained for a two-parameter exponentiated Pareto distribution for when samples are available from complete, type I and type II censoring schemes. Bayes estimators have been developed under a squared error loss function as well as under a LINEX loss function using priors of non-informative type for the parameters. It has been seen that the estimators obtained are not available in nice closed forms, although they can be easily evaluated for a given sample by using suitable numerical methods. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under squared error as well as under LINEX loss functions.     

Role of weights in improving the efficiency of Kim and Warde's mixed randomized response model

ABSTARCT

In this paper we have suggested a class of unbiased estimators of π_S, the proportion of respondents possessing a sensitive attribute A using mixed randomized response model. The variance of the proposed class of estimators has been obtained. In addition to Kim and Warde's (2005) estimator, several other acceptable estimators of π_S have been identified from the proposed class for suitable weights. It has been shown that the newly identified estimators are more efficient than the Kim and Warde's (2005) estimator. Numerical illustrations and graphs are also given in support of the present study.     

An improved alternative estimation procedure for current population mean in presence of positively and negatively correlated auxiliary variables in two-occasion rotation patterns

Abstract

The present study confirms the influential role of a positively and a negatively correlated auxiliary variables in enhancing the precision of estimates of current population mean in two occasion rotation (successive) sampling. Exponential-type estimators of current population mean have been proposed for three different situations: (i) the information on a positively correlated auxiliary variable is readily available on both occasions (ii) the information on a negatively correlated auxiliary variable is readily available on both occasions and (iii) the information on both positively and negatively correlated auxiliary variables are readily available on both the occasions. The characteristics of the proposed estimators have been explored and their efficacious performances are compared with the natural and recent contemporary estimators. Optimum replacement strategies of the proposed estimation procedures have been formulated. Simulation and empirical studies are carried out to justify the proposition of the proposed estimators and appropriate recommendations have been put forward to the survey practitioners.     

Generalized ratio-type and ratio-exponential-type estimators for population mean under modified Horvitz-Thompson estimator in adaptive cluster sampling

In the present article, we propose the generalized ratio-type and generalized ratio-exponential-type estimators for population mean in adaptive cluster sampling (ACS) under modified Horvitz-Thompson estimator. The proposed estimators utilize the auxiliary information in combination of conventional measures (coefficient of skewness, coefficient of variation, correlation coefficient, covariance, coefficient of kurtosis) and robust measures (tri-mean, Hodges-Lehmann, mid-range) to increase the efficiency of the estimators. Properties of the proposed estimators are discussed using the first order of approximation. The simulation study is conducted to evaluate the performances of the estimators. The results reveal that the proposed estimators are more efficient than competing estimators for population mean in ACS under both modified Hansen-Hurwitz and Horvitz-Thompson estimators.     

Bias-adjustment and calibration of jackknife variance estimator in the presence of non-response

In this paper, bias-adjustment in the jackknife estimator of variance accredited to Rao and Sitter (1995) has been considered. Then the bias-adjusted Rao and Sitter (1995) estimator has been calibrated such that its expected value under the imputing superpopulation model remains the same as the expected value of the mean squared error of the ratio estimator in the presence of non-response. A simulation study has been performed to compare the six different estimators of variance: out of them four estimators belong to Rao and Sitter (1995) and the other two proposed estimators are named as bias-adjusted and bias-adjusted-cum-calibrated estimators. The empirical relative bias and empirical relative efficiency of the two proposed estimators with respect to the four existing estimators accredited to Rao and Sitter (1995) have been investigated through simulations. The bias-adjusted-cum-calibrated estimator has been found to be an efficient estimator in the case of heteroscadastic populations. The present paper considers the situation of simple random and without replacement sampling. The possibility of obtaining a negative estimate of variance by the estimator due to Kim et al. (2006) has been pointed out.     

Some efficient classes of estimators of population mean in two-phase successive sampling under random non response

In this paper, an attempt has been made to present some efficient classes of estimators of population mean on current occasion in two-occasion successive sampling under random non response in two-phase setup. Effectiveness of the proposed classes of estimators has been studied under the assumptions that sampling units follow a distribution under the random non response. To check the performances, the proposed classes of estimators are compared with an estimator under the similar situation under the complete response. Results are demonstrated through empirical studies which show the reliable nature of the proposed classes of estimators. Suitable recommendations have been made to the survey practitioners.     

A Class of Estimators of Population Variance Using Auxiliary Information in Sample Surveys

This article advocates the problem of estimating the population variance of the study variable using information on certain known parameters of an auxiliary variable. A class of estimators for population variance using information on an auxiliary variable has been defined. In addition to many estimators, usual unbiased estimator, Isaki's (1983), Upadhyaya and Singh's (1999), and Kadilar and Cingi's (2006) estimators are shown as members of the proposed class of estimators. Asymptotic expressions for bias and mean square error of the proposed class of estimators have been obtained. An empirical study has been carried out to judge the performance of the various estimators of population variance generated from the proposed class of estimators over usual unbiased estimator, Isaki's (1983), Upadhyaya and Singh's (1999) and Kadilar and Cingi's (2006) estimators.