Search

In sample surveys that collect information on skewed variables, it is often desirable to assess the influence of sample units on the sampling error of survey-weighted estimators of finite population parameters. The conditional bias is an attractive measure of influence that accounts for the sampling design and the estimation method. It is defined as the design expectation of the sampling error conditional on a given unit being selected in the sample. The estimation of the conditional bias is relatively straightforward for simple sampling designs and estimators. However, for complex designs or complex estimators, it may be tedious to derive an explicit expression for the conditional bias. In those complex surveys, variance estimation is often achieved through replication methods such as the bootstrap. Bootstrap methods of variance estimation are typically implemented by producing a set of bootstrap weights that is provided to users along with the survey data. In this article, we show how to use these bootstrap weights to obtain an estimator of the conditional bias. Our bootstrap estimator is evaluated in a simulation study and illustrated using data from the Canadian Survey of Household Spending. [ABSTRACT FROM AUTHOR]

Differential privacy is a restriction on data processing algorithms that provides strong confidentiality guarantees for individual records in the data. However, research on proper statistical inference, that is, research on properly quantifying the uncertainty of the (noisy) sample estimate regarding the true value in the population, is currently still limited. This article proposes and evaluates several strategies to compute valid differentially private confidence intervals for the median. Instead of computing a differentially private point estimate and deriving its uncertainty, we directly estimate the interval bounds and discuss why this approach is superior if ensuring privacy is important. We also illustrate that addressing both sources of uncertainty—the error from sampling and the error from protecting the output—simultaneously should be preferred over simpler approaches that incorporate the uncertainty in a sequential fashion. We evaluate the performance of the different algorithms under various parameter settings in extensive simulation studies and demonstrate how the findings could be applied in practical settings using data from the 1940 Decennial Census. [ABSTRACT FROM AUTHOR]