Imputation by power transformation

In this paper, a new power transformation estimator of population mean in the presence of non-response has been suggested. The estimator of mean obtained from proposed technique remains better than the estimators obtained from ratio or mean methods of imputation. The mean squared error of the resultant estimator is less than that of the estimator obtained on the basis of ratio method of imputation for the optinum choice of parameters. An estimator for estimating a parameter involved in the process of new method of imputation has been discussed. The MSE expressions for the proposed estimators have been derived analytically and compared empirically. Product method of imputation for negatively correlated variables has also been introduced. The work has been extended to the case of multi-auxiliary information to be used for imputation.     

Estimation of sensitivity level of personal interview survey questions

In this paper, an optional randomized response model is proposed. The estimator of the mean of the stigmatized variable based on the optional randomized response sampling is shown to be more efficient than the usual estimator of the mean based on randomized response technique method. In addition to estimating population mean and variance, it has been shown that the optional randomized response technique is useful in quantifying the sensitivity levels of the questions in the personal interview surveys. An estimator for the sensitivity level of a question is proposed and an empirical study is carried out to show the validity of the proposed estimation technique. We also propose a test for the sensitivity level of the stigmatized variable.     

A dual problem of calibration of design weights

In this note, a dual problem to the calibration of design weights of the Deville and Särndal [Calibration estimators in survey sampling, J. Amer. Statist. Assoc. 87 (1992), pp. 376–382] method has been considered. We conclude that the chi-squared distance between the design weights and the calibrated weights equals the square of the standardized Z-score obtained by the difference between the known population total of the auxiliary variable and its corresponding Horvitz and Thompson [A generalization of sampling without replacement from a finite universe, J. Amer. Statist. Assoc. 47 (1952), pp. 663–685] estimator divided by the sample standard deviation of the auxiliary variable to obtain the linear regression estimator in survey sampling.     

Generalized franklin's model for randomized response sampling

In this paper we introduce two estimators of a population proportion when randomized response sampling with a normal randomizing distribution is used* The estimators have been obtained by using the method of moments. Both of the proposed estimators are shown to be more efficient than the corresponding estimators of Eranklin (1989 b).     

Two-step calibration of design weights in survey sampling

ABSTRACT

In this article, a new two-step calibration technique of design weights is proposed. In the first step, the calibration weights are set proportional to the design weights in a given sample. In the second step, the constants of proportionality are determined based on different objectives of the investigator such as bias reduction or minimum mean squared error. Many estimators available in the literature can be shown to be special cases of the proposed two-step calibrated estimator. A simulation study, based on a real data set, is also included at the end. A few technical issues are raised with respect to the use of the proposed calibration technique: both limitations and benefits are discussed.     

Calibration of the estimators of variance

This investigation suggests new techniques to calibrate estimators of variance. Estimators of the variance of simple mean, ratio and regression estimators under different sampling schemes are shown to be special cases of the proposed calibration techniques. The approach has more practical use due to recent advances in programming techniques and computational speed. An empirical study has been carried out to address the properties of these proposed strategies.     

Randomized response techniques: An application to the Botswana AIDS impact survey

The performance of the sampling strategy used in the Botswana Aids Impact Survey II (BAISII) has been studied in detail under a randomized response technique. We have shown that alternative strategies based on the Rao–Harley–Cochran (RHC) sampling scheme for the selection of first stage units perform much better than other strategies. In particular, the combination RHC for the selection of first stage units (fsu's) and systematic sampling for the selection of second stage units (ssu's) perform the best when the sample size is small where as the RHC and SRSWOR perform the best when the sample size is large. In view of the present findings it is recommended that the BAISII survey should be studied in more detail incorporating more indicators and increased sample sizes. This is because the BAISII survey design is extensively in use for large scales surveys in Southern African countries.     

Multi-character survery using randomized response technique

In the present paper, we have consisdered the situation of multi–character survey where the study variables, beside being poorly correlated with the selection probabilities are also sensitive in nature. Randomized Response technique (RRT) proposed by Chaudhuri and Adhikary (1990) is used to elicit the information on the sensitive character. The empirical study carried out shows the relative efficiency of the transformation suggested by Basnel and Singh (1985) over the transformations suggested by Rao (1966) and Amahia et al.(1989) under a super population model.     

Median Estimation Using Double Sampling

This paper proposes a general class of estimators for estimating the median in double sampling. The position estimator, stratification estimator and regression type estimator attain the minimum variance of the general class of estimators. The optimum values of the first-phase and second-phase sample sizes are also obtained for the fixed cost and the fixed variance cases. An empirical study examines the performance of the double sampling strategies for median estimation. Finally, an extension of the methods of Chen & Qin (1993) and Kuk & Mak (1994) is considered for the double sampling strategy.     

Estimation of Population Mean in the Presence of Linear Trend

The present article deals with some methods for estimation of finite populations means in the presence of linear trend among the population values. As a result, we provided a strategy for the selection of sampling interval k for the case of circular systematic sampling, which ensures better estimator for the population mean compared to other choices of the sampling interval. This has been established based on empirical studies. Further we more, applied multiple random starts methods for selecting random samples for the case of linear systematic sampling and diagonal systematic sampling schemes. We also derived the explicit expressions for the variances and their estimates. The relative performances of simple random sampling, linear systematic sampling and diagonal systematic sampling schemes with single and multiple random starts are also assessed based on numerical examples.