Improved two phase sampling exponential ratio and product type estimators for population mean of study character in the presence of non response

Improved two phase sampling exponential ratio and product type estimators for population mean using known coefficient of variation of study character in the presence of non response have been proposed and their properties are studied under large sample approximation. The proposed estimators are compared with the other existing estimators by using the MSE criterion and the conditions under which the proposed estimators perform better are obtained. An empirical study is also given to judge the performance of the proposed estimators. At the end, simulation studies have been carried out to verify the superiority to the proposed estimators.     

Combining information from multiple surveys by using regression for efficient small domain estimation

Summary.  In sample surveys of finite populations, subpopulations for which the sample size is too small for estimation of adequate precision are referred to as small domains. Demand for small domain estimates has been growing in recent years among users of survey data. We explore the possibility of enhancing the precision of domain estimators by combining comparable information collected in multiple surveys of the same population. For this, we propose a regression method of estimation that is essentially an extended calibration procedure whereby comparable domain estimates from the various surveys are calibrated to each other. We show through analytic results and an empirical study that this method may greatly improve the precision of domain estimators for the variables that are common to these surveys, as these estimators make effective use of increased sample size for the common survey items. The design-based direct estimators proposed involve only domain-specific data on the variables of interest. This is in contrast with small domain (mostly small area) indirect estimators, based on a single survey, which incorporate through modelling data that are external to the targeted small domains. The approach proposed is also highly effective in handling the closely related problem of estimation for rare population characteristics.     

Nonparametric estimation of the bivariate survival function with left-truncated and right-censored data

In this note, we consider estimating the bivariate survival function when both components are subject to left truncation and right censoring. We propose two types of estimators as generalizations of the Dabrowska and Campbell and Földes estimators. The consistency of the proposed estimators is established. A simple bootstrap method is used for obtaining precision estimation of the proposed estimators. A simulation study is conducted to investigate the performance of the proposed estimators.     

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.     

Estimation of a population size through capture-mark-recapture method: a comparison of various point and interval estimators

This article deals with the estimation of a fixed population size through capture-mark-recapture method that gives rise to hypergeometric distribution. There are a few well-known and popular point estimators available in the literature, but no good comprehensive comparison is available about their merits. Apart from the available estimators, an empirical Bayes (EB) estimator of the population size is proposed. We compare all the point estimators in terms of relative bias and relative mean squared error. Next, two new interval estimators – (a) an EB highest posterior distribution interval and (b) a frequentist interval estimator based on a parametric bootstrap method, are proposed. The comparison is then carried among the two proposed interval estimators and interval estimators derived from the currently available estimators in terms of coverage probability and average length (AL). Based on comprehensive numerical results, we rank and recommend the point estimators as well as interval estimators for practical use. Finally, a real-life data set for a green treefrog population is used as a demonstration for all the methods discussed.     

Robust estimation of AR coefficients under simultaneously influencing outliers and missing values

A family of robust estimators for coefficients of Gaussian AR(p) time series under simultaneously influencing distortions of two types: outliers and missing values, is proposed. The estimators are based on special properties of the Cauchy probability distribution; consistency and the asymptotic normality of these estimators are proven. An approximate solution of the problem of minimization of the asymptotic variance within the proposed family of estimators is found. Performance of the proposed estimators is illustrated for simulated time series and for real data sets.     

Fractional principal components regression: a general approach to biased estimators

Several biased estimators have been proposed as alternatives to the least squares estimator when multicollinearity is present in the multiple linear regression model. The ridge estimator and the principal components estimator are two techniques that have been proposed for such problems. In this paper the class of fractional principal component estimators is developed for the multiple linear regression model. This class contains many of the biased estimators commonly used to combat multicollinearity. In the fractional principal components framework, two new estimation techniques are introduced. The theoretical performances of the new estimators are evaluated and their small sample properties are compared via simulation with the ridge, generalized ridge and principal components estimators     

Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables

In this article, we propose a new class of estimators to estimate the finite population mean by using two auxiliary variables under two different sampling schemes such as simple random sampling and stratified random sampling. The proposed class of estimators gives minimum mean squared error as compared to all other considered estimators. Some real data sets are used to observe the performances of the estimators. We show numerically that the proposed class of estimators performs better as compared to all other competitor estimators.     

Optimal Change-point Estimation in Inverse Problems

We develop a method of estimating a change-point of an otherwise smooth function in the case of indirect noisy observations. As two paradigms we consider deconvolution and non-parametric errors-in-variables regression. In a similar manner to well-established methods for estimating change-points in non-parametric regression, we look essentially at the difference of one-sided kernel estimators. Because of the indirect nature of the observations we employ deconvoluting kernels. We obtain an estimate of the change-point by the extremal point of the differences between these two-sided kernel estimators. We derive rates of convergence for this estimator. They depend on the degree of ill-posedness of the problem, which derives from the smoothness of the error density. Analysing the Hellinger modulus of continuity of the problem we show that these rates are minimax     

Moments of the poly-Cauchy density with applications in estimation

Summary Simple mathematical formulae for the mean and variance of a poly-Cauchy density (proportional to a product of two Cauchy densities) are derived here and then applied to obtain Bayesian estimators for the mean of a normal population and the difference between means of two normal populations. The proposed estimators are arguably superior to the traditional estimators and to the usual Bayesian estimators, and may be highly robust.     

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.     

Estimation of Population Mean Under Non Response in Two-Occasion Rotation Patterns

The present article is an attempt to study the effect of non response at both occasions in search of good rotation patterns over two occasions. Ratio-type estimators were proposed for estimating the population mean at current occasion in presence of non response at both the occasions in two-occasion successive (rotation) sampling. Detail behaviors of proposed estimators were studied. Proposed estimators were compared with the estimator using no information from previous (first) occasion. Performances of the proposed estimators were demonstrated via empirical studies.     

Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring

We consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtub-shaped distribution on the basis of progressive type-II censored sample. The maximum likelihood estimators and Bayes estimators are derived for two unknown parameters, reliability function and hazard function. The Bayes estimators are obtained against squared error, LINEX and entropy loss functions. Also, using the Lindley approximation method we have obtained approximate Bayes estimators against these loss functions. Some numerical comparisons are made among various proposed estimators in terms of their mean square error values and some specific recommendations are given. Finally, two data sets are analyzed to illustrate the proposed methods.     

Estimation of Mean of Sensitive Characteristics for Successive Sampling

In this article, new estimators for estimating the population mean of a sensitive variable using the concept of successive sampling over two occasions are proposed. The unbiasedness and the variance properties of the proposed estimators are investigated analytically as well as numerically.     

Improved estimators for the common mean and ordered means of two normal distributions with ordered variances

We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959). Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators which take into account both order restrictions. However, in estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is discussed.     

Estimation of the bivariate cause-specific distribution function with doubly censored competing risks data

In this article, we consider estimating the bivariate cause-specific distribution function when both components are subject to double censoring. We propose two types of estimators as generalizations of the Dabrowska and Campbell and Földes estimators. The asymptotical properties of the proposed estimators are established. A simulation study is conducted to investigate the performance of the proposed estimators.     

Two new estimators of entropy for testing normality

ABSTRACT

We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the existing entropy estimators. Also, we propose two new tests for normality based on the introduced entropy estimators and compare their powers with the powers of other tests for normality. The results show that the proposed estimators and test statistics perform very well in estimating entropy and testing normality. A real example is presented and analyzed.     

A generalized class of estimators under two-phase stratified sampling for non response

In this paper, we propose a generalized class of estimators for finite population mean using two auxiliary variables in two-phase stratified sampling for non response. We identify 17 estimators as special cases of the proposed class of estimators. Expressions for the bias and mean squared error (MSE) of estimators are obtained up to first order of approximation. A data set is used for efficiency comparisons.     

Bias reduction in kernel density estimation

In this paper, we propose two kernel density estimators based on a bias reduction technique. We study the properties of these estimators and compare them with Parzen–Rosenblatt's density estimator and Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009, ‘The stochastic approximation method for the estimation of a multivariate probability density’, J. Statist. Plann. Inference, 139, 2459–2478) is density estimators. It turns out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the two classical estimators and the asymptotic MISE (Mean Integrated Squared Error) will be smaller than the two classical estimators. We corroborate these theoretical results through simulations.     

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.