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Data Fission: Splitting a Single Data Point
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DOI：10.1080/01621459.2023.2270748.png)
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Abstract
En 中文
Suppose we observe a random vector X from some distribution in a known family with unknown parameters. We ask the following question: when is it possible to split X into two pieces f(X) and g(X) such that neither part is sufficient to reconstruct X by itself, but both together can recover X fully, and their joint distribution is tractable? One common solution to this problem when multiple samples of X are observed is data splitting, but Rasines and Young offers an alternative approach that uses additive Gaussian noise-this enables post-selection inference in finite samples for Gaussian distributed data and asymptotically when errors are non-Gaussian. In this article, we offer a more general methodology for achieving such a split in finite samples by borrowing ideas from Bayesian inference to yield a (frequentist) solution that can be viewed as a continuous analog of data splitting. We call our method data fission, as an alternative to data splitting, data carving and p-value masking. We exemplify the method on several prototypical applications, such as post-selection inference for trend filtering and other regression problems, and effect size estimation after interactive multiple testing. Supplementary materials for this article are available online.
Keywords:
Mathematical statistics
Model selection/variable selection
Multiple comparisons
Regression
Journal
J
IF:
3
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5.1K
Citations:
4.8W