Joint influence of measurement error and non response on estimation of population mean

In this paper, we propose a method to jointly incorporate measurement error and non response in the estimators of population mean using auxiliary information in simple random sampling. We have not only studied some available estimators but also suggested three new estimators in the presence of two types of non sampling errors occurring jointly: the measurement error and the non response. The expressions for the bias and mean square errors of proposed estimator have been derived. A comparative study is made among the proposed estimators, the Hansen and Hurwitz (1946 Hansen, M.H., Hurwitz, W.N. (1946). The problem of non-response in sample surveys. J. Am. Stat. Assoc. 41:517–529.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator, the Cochran's (1977 Cochran, W.G. (1977). Sampling Techniques, 3rd Edn. New York: John Wiley &; Sons, Inc. [Google Scholar]) estimator, and the Singh and Kumar (2008 Singh, H.P., Karpe, N. (2008). Estimation of population variance using auxiliary information in the presence of measurement errors. Stat. Trans. New Ser. 9(3):443–470. [Google Scholar]) estimator.     

Estimation of population mean in presence of random non response in two-stage cluster sampling

The present investigation addresses the problem of estimating a finite population mean in two-phase cluster sampling in presence of random non response situations. Utilizing information on an auxiliary variable, regression type estimators has been proposed. Effective imputation techniques have been suggested to deal with the random non response situations. The properties of the proposed estimation strategies have been studied for different cases of random non response situations in practical surveys. The superiority of the suggested methodology over the natural sample mean estimator of population mean has been established through empirical studies carried over the data sets of natural population and artificially generated population.     

Estimation of population mean based on dual use of auxiliary information in non response

Whenever there is auxiliary information available in any form, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. When there exists enough amount of correlation between the study and the auxiliary variables, and parallel to these associations, the ranks of the auxiliary variables are also correlated with the study variable, which can be used a valuable device for enhancing the precision of an estimator accordingly. This article addresses the problem of estimating the finite population mean that utilizes the complementary information in the presence of (i) the auxiliary variable and (ii) the ranks of the auxiliary variable for non response. We suggest an improved estimator for estimating the finite population mean using the auxiliary information in the presence of non response. Expressions for bias and mean squared error of considered estimators are derived up to the first order of approximation. The performance of estimators is compared theoretically and numerically. A numerical study is carried out to evaluate the performances of estimators. It is observed that the proposed estimator is more efficient than the usual sample mean and the regression estimators, and some other families of ratio and exponential type of estimators.     

Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and non-response

Most of the research work in the theory of survey sampling only deals with the sampling errors under the assumptions: (i) there is a complete response and (ii) recorded information from individuals is correct but in practice it is not always true. Non-sampling errors like non-response and measurement errors (MEs) mostly creep into the survey and become more influential for estimators than sampling errors. Considering this practical situation of non-response and MEs jointly, we proposed an optimum class of estimators for population mean under simple random sampling using conventional and non-conventional measures. Bias and mean square error of the proposed estimators are derived up to first degree of approximation. Moreover, a simulation study is conducted to assess the performance of new estimators which proves that proposed estimators are more efficient than the traditional Hansen and Hurwitz estimator and other competing estimators.     

Empirical likelihood inference in the presence of measurement error

Suppose that several different imperfect instruments and one perfect instrument are used independently to measure some characteristic of a population. The authors consider the problem of combining this information to make statistical inference on parameters of interest, in particular the population mean and cumulative distribution function. They develop maximum empirical likelihood estimators and study their asymptotic properties. They also present simulation results on the finite sample efficiency of these estimators.     

Estimation of population mean on the most recent occasion under non response in h-occasion successive sampling using several auxiliary variables

In this article, general estimation procedures of population mean on the most recent occasion in the presence of non response on all occasions have been deduced in h-occasion successive sampling. In the estimation procedures, regression type estimators have been suggested with the aid of stable and mutually independent several auxiliary variables which are readily available only on the most recent occasion. To check the efficiency of the proposed estimators, they have been compared with similar estimator in absence of non response. Properties of the suggested estimation procedures have been studied and their empirical studies are carried out to validate the theoretical results. Suitable recommendations have been made.     

Estimation of population mean in two-occasion successive sampling

In the present article, we have proposed some classes of estimators based on transformed auxiliary variable. The biases and mean squared errors (MSEs) of the proposed estimators have been obtained. The proposed estimators have been compared with simple mean estimator when there is no matching and the optimum estimator, which is a combination of the means of the matched and unmatched portion of the sample at the second occasion. Optimum replacement policy and the efficiency of the proposed estimators have been discussed. Theoretical results are well supported with an empirical study.     

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.     

A class of exponential-type ratio estimators of a general parameter

This paper addresses the problem of estimating a general parameter using information on an auxiliary variable X. We have suggested a class of exponential-type ratio estimators for the parameter and its properties are studied. It is identified that the estimators due to Upadhyaya et al. [Journal of Statistical Theory and Practice (2011), 5(2), 285–302] and Yadav and Kadilar [Revista Columbiana de Estadistica, (2013), 36(1), 145–152] are members of the proposed estimator. We have also shown that the suggested estimator is more efficient than the estimators of Upadhyaya et al. (2011 Upadhyaya, L.N., Singh, H.P., Chatterjee, S., Yadav, R. (2011). Improved ratio and product exponential type estimators. J. Stat. Theo. Pract. 5 (2): 285–302.[Taylor &; Francis Online] , [Google Scholar]) and Yadav and Kadilar (2013 Yadav, S.K., Kadilar, C. (2013). Improved exponential type ratio estimator of population variance. Revis. Colum. de Estadist. 36(1): 145–152. [Google Scholar]). Numerical illustration is provided in support of the present study.     

Mean intergrated squared error properties and optimal kernels when estimating a diatribution function

Let X₁,X₂,… X_n be a sample of independent identically distributed (i.i.d)random variables having an unknown absolutely continuous distribution function f with density f the twofold aim of his paper consists in, firstly deriving asymptotic expressions of the mean intergrated squared error (MISE) of a kernel estimator of F when f is either assumed to be continuous everywhere or problem of finding optimal kernels in these two cases is studied in detail.     

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.     

Estimation of population mean in successive sampling under super-population model in presence of random non response situations

The present work is an attempt to estimate the population mean on the current occasion in two-occasion successive (rotation) sampling in presence of random non response situations. The estimation strategy has been constructed under a super-population model design approach with the help of imputation technique. The estimators proposed on the current occasion cover the cases of occurrences random non responses on either of the occasions. Detail behaviors of the proposed class of estimators have been studied and its performance has been examined with the sample mean estimator. The results are demonstrated through empirical studies which establish the effectiveness of the proposed class of estimators. Suitable recommendations have been put forward to the survey statisticians for its practical application.     

Estimation of finite population mean in stratified sampling using scrambled responses in the presence of measurement errors

This study focuses on the estimation of population mean of a sensitive variable in stratified random sampling based on randomized response technique (RRT) when the observations are contaminated by measurement errors (ME). A generalized estimator of population mean is proposed by using additively scrambled responses for the sensitive variable. The expressions for the bias and mean square error (MSE) of the proposed estimator are derived. The performance of the proposed estimator is evaluated both theoretically and empirically. Results are also applied to a real data set.     

Estimation of mean vector in presence of non-response

Simultaneous estimation of means of several variables is considered for finite population in presence of non-response. Two types of nonresponses (partial and complete) are considered using the technique of sampling and subsampling with equal probabilities without replacement. The optimum sample size and the optimum value of subsampling fraction to be repeated from the nonresponding units of the sample have been obtained for fixed survey budget.     

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.     

Modal non‐linear regression in the presence of Laplace measurement error

In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error. Starting with the modal regression procedure developed for the measurement error‐free case, a non‐trivial modification is made so that the modified version can effectively correct the potential bias caused by measurement error. Large sample properties of the proposed estimate, such as the convergence rate and the asymptotic normality, are thoroughly investigated. A simulation study and real data application are conducted to illustrate the satisfying finite sample performance of the proposed estimation procedure.     

Effectual variance estimation strategy in two-occasion successive sampling in presence of random non response

Present investigation deals with the problem of random non response in estimation of population variance on current occasion in two-occasion successive sampling. To reduce the negative impact of random non response on both occasions, regression type imputation method has been suggested. Using auxiliary information, efficient estimation strategies have been developed for estimation of population variance on the current occasion. Estimator for the population variance is also derived as a special case when random non response occurs only on the current occasion. Empirical studies are carried out to show the dominance of suggested estimators over sample variance and exponential type estimators. Results are interpreted.