Differentially Private Confidence Intervals for Population Proportions under Stratified Random Sampling

Основні поняття

The authors propose three differentially private algorithms for constructing confidence intervals for population proportions under stratified random sampling, providing privacy guarantees and asymptotic coverage properties.

Анотація

The paper focuses on developing differentially private confidence intervals for population proportions under stratified random sampling. It presents three algorithms that add noise at different levels (stratum or population) to achieve differential privacy, depending on whether the sample sizes are public or private.

The key highlights and insights are:

1. The authors articulate two variants of differential privacy that are appropriate for data from stratified sampling designs: "substitute-one relation within a stratum" and "remove/add-one relation".

2. The proposed algorithms propagate the uncertainty due to the application of differentially private mechanisms into the construction of confidence intervals, with necessary bias corrections to achieve asymptotic unbiased variance estimates.

3. Theoretical results are provided to guarantee the desired privacy level and asymptotic coverage properties of the confidence intervals under each algorithm.

4. The authors analyze and compare the additional variance introduced by the noise addition across the three algorithms, relating it to the sampling weights.

5. Simulation studies and two applications to the 1940 Census data are conducted to evaluate the performance of the proposed private confidence intervals.

Overall, the paper establishes the first rigorous methodologies on differentially private confidence intervals in the context of survey sampling, which is an important area in statistics.

Статистика

None.

Цитати

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Ключові висновки, отримані з

Differentially Private Confidence Intervals for Proportions under Stratified Random Sampling

by Shurong Lin,... о arxiv.org 04-12-2024

https://arxiv.org/pdf/2301.08324.pdf

Глибші Запити

How can the proposed algorithms be extended to construct differentially private confidence intervals for other survey sampling designs beyond stratified random sampling

To extend the proposed algorithms for constructing differentially private confidence intervals to other survey sampling designs beyond stratified random sampling, we can consider adapting the noise addition mechanisms based on the specific characteristics of the new sampling designs. Here are some ways to extend the algorithms:

Cluster Sampling: For cluster sampling, where clusters of individuals are sampled rather than individual units, we can modify the algorithms to add noise at the cluster level instead of the individual level. This would involve adjusting the sensitivity calculations and noise addition strategies to account for the cluster structure.

Systematic Sampling: In systematic sampling, every nth individual is selected from the population. The algorithms can be modified to incorporate the systematic sampling design by adjusting the noise addition process to reflect the systematic selection process.

Multistage Sampling: For complex multistage sampling designs involving multiple levels of sampling, the algorithms can be extended to add noise at each stage of sampling. This would require careful consideration of the privacy guarantees at each stage and the overall impact on the final confidence interval.

Stratified Cluster Sampling: In designs combining stratification and clustering, a combination of the noise addition strategies for stratified and cluster sampling can be employed to ensure differential privacy while accounting for both stratification and clustering effects.

By customizing the noise addition mechanisms and sensitivity calculations to suit the specific features of different survey sampling designs, the proposed algorithms can be effectively extended to construct differentially private confidence intervals for a wide range of survey designs.

What are the potential challenges and considerations in applying these differentially private confidence interval methods to real-world survey data with complex sampling designs

Applying differentially private confidence interval methods to real-world survey data with complex sampling designs poses several challenges and considerations:

Privacy-Utility Trade-Off: Balancing the trade-off between privacy and utility is crucial. Increasing privacy by adding more noise may lead to wider confidence intervals and reduced precision in estimates, impacting the usefulness of the results.

Accuracy and Bias: Ensuring that the added noise does not introduce significant bias in the estimates is essential. Careful calibration of the noise levels is required to maintain accuracy while preserving privacy.

Sample Size and Heterogeneity: Dealing with varying sample sizes across strata or clusters, as well as the heterogeneity of the population, can complicate the application of these methods. Adjustments may be needed to account for unequal sampling probabilities and population characteristics.

Complex Survey Designs: Handling intricate survey designs involving stratification, clustering, and weighting requires a comprehensive understanding of the design effects and their impact on the estimation process. Adapting the algorithms to accommodate these complexities is essential.

Data Quality and Missing Data: Addressing issues related to data quality, missing data, and non-response in survey data is crucial for accurate estimation. Incorporating mechanisms to handle missing data while maintaining privacy is a key consideration.

By addressing these challenges and considerations thoughtfully, the application of differentially private confidence interval methods to real-world survey data with complex sampling designs can yield valuable insights while safeguarding individual privacy.

How can the insights from this work on differentially private confidence intervals be leveraged to develop privacy-preserving statistical inference procedures for other survey-based analyses beyond just proportions

The insights gained from the development of differentially private confidence intervals can be leveraged to enhance privacy-preserving statistical inference procedures for various survey-based analyses beyond proportions. Here are some ways to extend these insights:

Estimation of Means and Totals: The methodologies can be adapted to estimate means, totals, and other population parameters while ensuring differential privacy. By modifying the noise addition mechanisms and sensitivity calculations, private estimators for these parameters can be developed.

Regression and Modeling: Extending the techniques to incorporate regression analysis and statistical modeling can enable the development of privacy-preserving predictive models and inference procedures. This involves incorporating privacy-preserving mechanisms into regression models and model fitting processes.

Complex Survey Estimation: Applying the principles of differential privacy to complex survey estimation techniques such as ratio estimation, domain estimation, and small area estimation can enhance the privacy guarantees of these methods. Customizing the algorithms to suit the specific requirements of these estimation procedures is essential.

Longitudinal and Panel Data: Adapting the algorithms to handle longitudinal and panel data analysis can provide privacy-preserving solutions for tracking changes over time and analyzing repeated measures data. Incorporating temporal aspects into the privacy mechanisms is crucial for maintaining privacy across multiple time points.

By leveraging the foundational concepts and methodologies developed for differentially private confidence intervals, a wide range of statistical inference procedures in survey-based analyses can be enhanced to ensure privacy protection while delivering reliable and accurate results.