Confidence interval for the sensitive fraction in Item Count Technique model

TL;DR

This paper develops an exact confidence interval for estimating the sensitive characteristic's prevalence using the Item Count Technique, balancing privacy protection and statistical precision.

Contribution

It introduces a method to construct an exact confidence interval for the sensitive fraction, considering privacy levels and sample size optimization.

Findings

Derived the exact confidence interval for the sensitive fraction.

Analyzed the relationship between privacy level, sample size, and interval length.

Provided guidelines for optimal sample size based on desired confidence interval length.

Abstract

The problem is in the estimation of the fraction of population with a sensitive characteristic. We consider the Item Count Technique an indirect method of questioning designed to protect respondents' privacy. The exact confidence interval for the sensitive fraction is constructed. The length of the proposed CI depends on both the given parameter of the model and the sample size. For these CI the model's parameter is established in relation to the provided level of the privacy protection of the interviewee. The optimal sample size for obtaining a CI of a given length is discussed in the context.