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.     

On use of symmetrical balanced incomplete block design in construction of sampling design realising pre-assigned sets of inclusion probabilities of first two orders.

Gupta, Nigam and Kumar (1982) proposed a sampling scheme using certain combinatorial properties of balanced incomplete block design (BIBD) which realises first order inclusion probabilities proportional to measure of size(IPPS). Here their results have been extended by presenting samplng schemes realising pre-assigned sets of inclusion probabilities of first two orders.     

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.     

On comutativity of design and model expectations in randomized response surveys

Interchangability of the order of design expectation ( E_p ) and model expectation ( E_R ) under randomized response ( RR ) surveys for finding expectation and mean-square error of a linear estimator e found to be permissible for a non-informative sampling design. The non-comutative property established by Chaudhuri & Adhikary ( 1990 ) under probability proportional to size with replacement ( PPSWR ) sampling is disproved.     

Empirical Performance of Cross-Validation With Oracle Methods in a Genomics Context

When employing model selection methods with oracle properties such as the smoothly clipped absolute deviation (SCAD) and the Adaptive Lasso, it is typical to estimate the smoothing parameter by m-fold cross-validation, for example, m = 10. In problems where the true regression function is sparse and the signals large, such cross-validation typically works well. However, in regression modeling of genomic studies involving Single Nucleotide Polymorphisms (SNP), the true regression functions, while thought to be sparse, do not have large signals. We demonstrate empirically that in such problems, the number of selected variables using SCAD and the Adaptive Lasso, with 10-fold cross-validation, is a random variable that has considerable and surprising variation. Similar remarks apply to non-oracle methods such as the Lasso. Our study strongly questions the suitability of performing only a single run of m-fold cross-validation with any oracle method, and not just the SCAD and Adaptive Lasso.     

Alternative Estimators for Randomized Response Techniques in Multi-Character Surveys

Tail estimates are developed for power law probability distributions with exponential tempering, using a conditional maximum likelihood approach based on the upper-order statistics. Tempered power law distributions are intermediate between heavy power-law tails and Laplace or exponential tails, and are sometimes called “semi-heavy” tailed distributions. The estimation method is demonstrated on simulated data from a tempered stable distribution, and for several data sets from geophysics and finance that show a power law probability tail with some tempering.     

Optional randomized response technique in two-phase sampling

Two-phase optional randomized response (TORR) technique has been proposed. The proposed randomized response (RR) performs much better in general than the existing RR techniques. Theoretical and numerical illustrations identified conditions of superiority of the proposed TORR over the existing comparable optional randomized response (ORR) techniques.     

Randomized response surveys: Optimum estimation of a finite population total

Randomized response (RR) techniques are used to gather information of a sensitive nature. Optimal sampling strategies for estimating a finite population total under a superpopulation model have been derived by utilizing auxiliary information suitably in constructing the RR techniques.     

Optimal Estimation of a Finite Population Total Under Randomized Response Surveys

Problems of estimation of a finite population total of a variable of sensitive in nature are studied under randomized response (RR) surveys. Some optimal sampling strategies are presented under different superpopulation models.     

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.