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An extension of the standardized randomized response technique to a multi-stage setup

机译：将标准化随机响应技术扩展到多阶段设置

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摘要

If nonresponse and/or untruthful answering mechanisms occur, analyzing only the available cases may substantially weaken the validity of sample results. The paper starts with a reference to strategies of empirical social researchers related to respondent cooperation in surveys embedding the statistical techniques of randomized response in this framework. Further, multi-stage randomized response techniques are incorporated into the standardized randomized response technique for estimating proportions. In addition to already existing questioning designs of this family of methods, this generalization includes also several (in particular: two-stage) techniques that have not been published before. The statistical properties of this generalized design are discussed for all probability sampling designs. Further, the efficiency of the model is presented as a function of privacy protection. Hence, it can be shown that not one multi-stage design of this family at the same level of privacy protection can theoretically be more efficient than its one-stage basic version.
机译：如果出现无应答和/或不正确的应答机制，仅分析可用案例可能会大大削弱样本结果的有效性。本文首先参考了与调查中被调查者合作相关的经验性社会研究者的策略，该策略将随机反应的统计技术嵌入该框架中。此外，将多阶段随机响应技术结合到标准化随机响应技术中以估计比例。除了该方法系列已经存在的疑问设计之外，这种概括还包括以前未曾公开的几种（特别是两阶段）技术。对于所有概率采样设计，都讨论了这种广义设计的统计特性。此外，模型的效率被表示为隐私保护的函数。因此，可以证明，在同一级别的隐私保护下，该家族的一个多阶段设计在理论上不会比其一级基本版本更有效。

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