Universal inference
Universal inference
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DOI：
10.1073/pnas.1922664117
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
L. Wasserman;Aaditya Ramdas;Sivaraman Balakrishnan
中科院分区：
文献类型：
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作者：
L. Wasserman;Aaditya Ramdas;Sivaraman Balakrishnan
意义
大多数统计方法依赖于某些数学条件，即正则性假设，以确保其有效性。没有这些条件，像P值和置信区间这样的统计量可能是无效的。在本文中，我们给出了一种令人惊讶的简单方法，用于在没有任何正则性条件的情况下得出统计显著性陈述。由此产生的假设检验可用于任何参数模型以及若干非参数模型。我们提出了一种通用方法，用于构建在没有正则性条件下具有有限样本保证的置信集和假设检验。我们将此类程序称为“通用的”。该方法非常简单，基于通常的似然比统计量的一个修改版本，我们称之为“分割似然比检验”（split LRT）统计量。当用于检验不规则统计模型中的复合零假设时，经典似然比统计量的（极限）零分布常常是难以处理的。我们的方法对于这些复杂情形下的统计推断特别有吸引力。我们提出的方法适用于任何参数模
型，也适用于一些非参数模型，只要在零假设下计算最大似然估计量（MLE）是可行的。在混合建模和形状约束推断中会出现典型的例子，对于这些情况，构建检验和置信集是出了名的困难。我们还对我们的基本方法进行了各种扩展。我们表明，在计算MLE困难的情况下，为了构建有效的检验和区间，对最大似然进行上界估计就足够了。我们研究了在模型误设情况下我们的方法能得出有效推断的一些条件。此外，分割似然比检验可与轮廓似然一起使用来处理讨厌参数，并且它也可顺序运行以产生随时有效的P值和置信序列。最后，当与筛法相结合时，它可用于对嵌套模型类进行模型选择。
Significance Most statistical methods rely on certain mathematical conditions, known as regularity assumptions, to ensure their validity. Without these conditions, statistical quantities like P values and confidence intervals might not be valid. In this paper we give a surprisingly simple method for producing statistical significance statements without any regularity conditions. The resulting hypothesis tests can be used for any parametric model and for several nonparametric models. We propose a general method for constructing confidence sets and hypothesis tests that have finite-sample guarantees without regularity conditions. We refer to such procedures as “universal.” The method is very simple and is based on a modified version of the usual likelihood-ratio statistic that we call “the split likelihood-ratio test” (split LRT) statistic. The (limiting) null distribution of the classical likelihood-ratio statistic is often intractable when used to test composite null hypotheses in irregular statistical models. Our method is especially appealing for statistical inference in these complex setups. The method we suggest works for any parametric model and also for some nonparametric models, as long as computing a maximum-likelihood estimator (MLE) is feasible under the null. Canonical examples arise in mixture modeling and shape-constrained inference, for which constructing tests and confidence sets has been notoriously difficult. We also develop various extensions of our basic methods. We show that in settings when computing the MLE is hard, for the purpose of constructing valid tests and intervals, it is sufficient to upper bound the maximum likelihood. We investigate some conditions under which our methods yield valid inferences under model misspecification. Further, the split LRT can be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid P values and confidence sequences. Finally, when combined with the method of sieves, it can be used to perform model selection with nested model classes.