Gaussian universal likelihood ratio testing

Summary The classical likelihood ratio test based on the asymptotic chi-squared distribution of log-likelihood is one fundamental tools statistical inference. A recent universal approach sample splitting provides valid hypothesis tests and confidence sets in any setting for which we can compute split statistic, or, more generally, an upper bound null maximum likelihood. finite samples without regularity conditions. This empowers statisticians to construct settings no previously existed. For simple, but fundamental, case testing population mean $d$-dimensional Gaussian data with identity covariance matrix, itself applies. Thus, this serves as a perfect bed compare against test. work presents first in-depth exploration size, power relationships between several variants. We show that repeated subsampling best choice terms size power. large numbers subsamples, set approximately spherical. observe reasonable performance even high-dimensional setting, where expected squared radius test’s 3/2 times spherical set. illustrate benefits through nonconvex doughnut-shaped hypothesis, inference procedure have higher than standard approach.