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We present simulated standard curves for the calibration of empirical likelihood ratio (ELR) tests of means. With the help of these curves, the nominal significance level of the ELR test can be adjusted in order to achieve (quasi-) exact type I error rate control for a given, finite sample size. By theoretical considerations and by computer simulations, we demonstrate that the adjusted significance level depends most crucially on the skewness and on the kurtosis of the parent distribution. For practical purposes, we tabulate adjusted critical values under several prototypical statistical models.
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters, and model
The likelihood ratio test (LRT) based on the asymptotic chi-squared distribution of the log likelihood is one of the fundamental tools of statistical inference. A recent universal LRT approach based on sample splitting provides valid hypothesis tests
The complexity underlying real-world systems implies that standard statistical hypothesis testing methods may not be adequate for these peculiar applications. Specifically, we show that the likelihood-ratio tests null-distribution needs to be modifie
The celebrated Bernstein von-Mises theorem ensures that credible regions from Bayesian posterior are well-calibrated when the model is correctly-specified, in the frequentist sense that their coverage probabilities tend to the nominal values as data
We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated coordinates.