比类型估计量在数量特征随机化回答技术中的应用

本文在数量特征随机化回答技术中当变异系数、偏度系数、峰度系数已知时,对总体均值提出了一系列比类型估计量,并且在一定条件下,证明了这些估计量优于Gupta et al.提出的估计量。     

Estimating population proportions in the presence of missing data

This paper discusses the estimation of a population proportion in the presence of missing data and using auxiliary information at the estimation stage. A general class of estimators, which make efficient use of the available information, are proposed. Some theoretical properties of the proposed estimators are analyzed, and they allow us to find the optimal value for the proposed class in the sense of minimal variance. The optimal estimator is thus more efficient than the customary estimator. Results derived from a simulation study indicate that the proposed optimal estimator gives desirable results in comparison to alternative estimators.     

有辅助信息时有限总体分布函数的新估计量

本文提出两个新的估计量,利用观察数据中的总体辅助信息来估计有限总体分布函数,并通过两个人工总体的模拟实验,比较新的估计量、传统的估计量及Rao,Kover&Mantel(1990)提出的估计量的相对平均误差与相对标准差。结果表明,从相对标准差的角度分析,两个新的估计量有一个是四个估计量中精度最好的一个,另一个也有很好的表现;而且它们在模型有所偏差时都具备了较好的稳健性。     

具有缺失数据的Eichhorn模型

为了解决在Eichhorn乘法扰动模型中存在的项目无回答问题,对敏感变量总体均值在辅助变量总体均值已知与未知条件下提出了比率插补方法.理论比较和数值模拟得出的结果表明提出的插补方法比传统的方法效率更高.     

Nonparametric additive model-assisted estimation for survey data

An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson estimators by combining the spline and local polynomial smoothing methods. These estimators are calibrated, asymptotically design-unbiased, consistent, normal and robust in the sense of asymptotically attaining the Godambe-Joshi lower bound to the anticipated variance. A consistent model selection procedure is further developed to select the significant auxiliary variables. The proposed method is sufficiently fast to analyze large survey data of high dimension within seconds. The performance of the proposed method is assessed empirically via simulation studies.     

A note on ratio and product type estimators

Summary The use of ratio and product estimators for the mean of a finite population is well known. This paper proposes transformed estimators obtained through parametric linear combination of the ratio, or product, and the usual unbiased estimator of the mean for any sample design. To the first degree of approximation, the proposed estimators have smaller mean square error than that of the ratio, product and the usual unbiased estimator, for suitable choice of the parameter. The superiority of the proposed estimators over others for small samples has been studied empirically.     

An improved class of estimators of a finite population quantile in sample surveys

This work proposes a general class of estimators for a finite population quantile using auxiliary information. This information is provided by the population means of auxiliary variables. The optimum estimator in this class is derived. This result is supported with a numerical example.     

An improved exponential estimator of finite population mean in simple random sampling using an auxiliary attribute

In this paper, we propose an exponential ratio type estimator of the finite population mean when auxiliary information is qualitative in nature. Under simple random sampling without replacement scheme, the expressions for the bias and the mean square error of the proposed estimator have been obtained, up to first order of approximation. To show that our proposed estimator is more efficient as compared to the existing estimators, we have made a comparative study with respect to their mean square errors. Theoretically and numerically, we have found that our proposed estimator is always more efficient as compared to its competitor estimators including all the estimators of Abd-Elfattah et al. [1] [A.M. Abd-Elfattah, E.A. El-Sherpieny, S.M. Mohamed, and O.F. Abdou. Improvement in estimating the population mean in simple random sampling using information on auxiliary attribute. Applied Mathematics and Computation, 215 (2010), 4198-4202].     

利用分层抽样数据中完全辅助信息的模型校正方法

In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator(or GREG).     

A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information

This paper considers the problem of estimating the finite-population distribution function and quantiles with the use of auxiliary information at the estimation stage of a survey. We propose the families of estimators of the distribution function of the study variate y using the knowledge of the distribution function of the auxiliary variate x. In addition to ratio, product and difference type estimators, many other estimators are identified as members of the proposed families. For these families the approximate variances are derived, and in addition, the optimum estimator is identified along with its approximate variance. Estimators based on the estimated optimum values of the unknown parameters used to minimize the variance are also given with their properties. Further, the family of estimators of a finite-population distribution function using two-phase sampling is given, and its properties are investigated.      

Regression estimation with transformed auxiliary variates

The regression estimation of the mean of a primary survey variable and the estimation of the regression equation are considered in the finite population with transformed auxiliary variables. Large sample properties of estimators are developed. The effects of estimating auxiliary variates on estimators are investigated.     

Generalized Calibration Approach for Estimating Variance in Survey Sampling

In the present investigation, a general set-up for inference from survey data that covers the estimation of variance of estimators of totals and distribution functions has been considered, using known higher order moments of auxiliary information at the estimation stage. Several estimators of variance of estimators of totals and distribution functions are shown to be the special cases of the proposed strategy. An empirical study has also been given to show the performance of the proposed estimators over the existing estimators in the literature.     

Missing data and auxiliary information in surveys

Summary  This paper proposes estimation methods with auxiliary information when some observations are missing from the sample. These ratio, difference and regression methods are proposed for any sampling design and are compared with other complete case estimators.     

Improvement in estimating the population mean in simple random sampling

This paper proposes some estimators for the population mean using the ratio estimators presented in [C. Kadilar, H. Cingi, Ratio estimators in simple random sampling, Applied Mathematics and Computation 151 (2004) 893–902] and shows that all proposed estimators are always more efficient than the ratio estimators. This result is also supported by a numerical example.     

Quantile estimation under successive sampling

This paper deals with the estimation, under sampling in two successive occasions, of a finite population quantile. For this sampling design a class of estimators is proposed whose the ratio and difference estimators are particular cases. Asymptotic variance formulae are derived for the proposed estimators, and the optimal matching fraction is discussed. Comparisons are made with existing estimators in a simulation study using a natural population.     

用辅助变量分层和将其用于比估计抽样效果的比较

本文给出用辅助变量构造比估计量的抽样效果优于用它分层的条件。     

On a class of almost unbiased ratio estimators

Summary Murthy and Nanjamma [4] studied the problem of construction of almost unbiased ratio estimators for any sampling design using the technique of interpenetrating subsamples. Subsequently, Rao [7], [8] has given a general method of constructing unbiased ratio estimators by considering linear combinations of the two simple estimators based on the ratio of means and the mean of ratios. However, it is difficult to choose an optimum weight (Rao [9]) which minimizes the variance of the combined estimator since the weights are random in certain cases. In this note, we consider a different method of combining these estimators and obtain a general class of almost unbiased ratio estimators of which Murthy and Nanjamma's is a particular case and derive an optimum in this class. The case of simple random sampling where a similar class of almost unbiased ratio estimators can be developed is briefly discussed. The results are illustrated by means of simple numerical examples.     

Model-based design in small area estimation

In this paper, we address the problem of an efficient estimation strategy when solving real survey sampling problems. We consider the panel data model with random effects as a superpopulation model. We investigate the performance of model-assisted estimators under model-based sample designs in a simulation experiment based on the real data (Lithuanian survey on short-term statistics on service) taken as a true population. Here the model-based sampling refers to a sample design constructed using the model and information about the behavior of the model-assisted estimator on available auxiliary data.     

Multivariate logistic regression with incomplete covariate and auxiliary information

In this article, we propose and explore a multivariate logistic regression model for analyzing multiple binary outcomes with incomplete covariate data where auxiliary information is available. The auxiliary data are extraneous to the regression model of interest but predictive of the covariate with missing data. Horton and Laird [N.J. Horton, N.M. Laird, Maximum likelihood analysis of logistic regression models with incomplete covariate data and auxiliary information, Biometrics 57 (2001) 34–42] describe how the auxiliary information can be incorporated into a regression model for a single binary outcome with missing covariates, and hence the efficiency of the regression estimators can be improved. We consider extending the method of [9] to the case of a multivariate logistic regression model for multiple correlated outcomes, and with missing covariates and completely observed auxiliary information. We demonstrate that in the case of moderate to strong associations among the multiple outcomes, one can achieve considerable gains in efficiency from estimators in a multivariate model as compared to the marginal estimators of the same parameters.     

A class of estimators with estimated optimum values in sample surveys

Srivastava and Jhajj (1981) proposed a class of estimators for population mean of a character using auxiliary information and optimum values involving unknown parameters. From the practical point of view, their results have very little utility. In view of practical utility, we propose a class of estimators with estimated optimum values. Further, it is shown that the proposed class with estimated optimum values attains the same minimum mean square error of the class of estimators based on optimum values.