In group average analyses, we generalize the classical one-sample t test to account for heterogeneous within-subject uncertainties associated with the estimated effects. Our test statistic is defined as the maximum likelihood ratio corresponding to a Gaussian mixed-effect model. The test's significance level is calibrated using the same sign permutation framework as in Holmes et al., allowing f...

Given an L-function, one of the most important questions concerns its vanishing at the central point; for example, the Birch and Swinnerton-Dyer conjecture states that the order of vanishing there of an elliptic curve L-function equals the rank of the Mordell-Weil group. The Katz and Sarnak Density Conjecture states that this and other behavior is well-modeled by random matrix ensembles. This c...

For many complex traits, single nucleotide polymorphisms (SNPs) identified from genome-wide association studies (GWAS) only explain a small percentage of heritability. Next generation sequencing technology makes it possible to explore unexplained heritability by identifying rare variants (RVs). Existing tests designed for RVs look for optimal strategies to combine information across multiple va...

Economists are often interested in estimating averages with respect to distributions of unobservables, such as moments individual fixed-effects, or average partial effects discrete choice models. For quantities, we propose and study posterior (PAE), where the is computed conditional on sample, spirit empirical Bayes shrinkage methods. While usefulness for prediction well-understood, a justifica...