We show that two popular selective inference procedures, namely data carving (Fithian et al., 2017) and selection with a randomized response (Tian et al., 2018b), when combined with the polyhedral method (Lee et al., 2016), result in confidence intervals whose length is bounded. This contrasts results for confidence intervals based on the polyhedral method alone, whose expected length is typically infinite (Kivaranovic and Leeb, 2020). Moreover, we show that these two procedures always dominate corresponding sample-splitting methods in terms of interval length.

翻译：我们发现两种流行的选择性推断程序,即数据刻录(Fithian等人,2017年)和随机响应(Tian等人,2018年b)选择(Tian等人,2018年b),如果与多面体方法相结合(Lee等人,2016年),就会形成隔间,其长度受限。这与仅以多面体方法为基础,其预期长度通常无限(Kivaranovic和Leeb,2020年)的隔间隔结果形成对比。 此外,我们证明这两种程序在间隔长度方面总是主导相应的样本分割方法。