We show that the naive mean-field approximation correctly predicts leading term of logarithmic lower tail probabilities for number copies a given subgraph in G(n,p) and arithmetic progressions length random subsets integers entire range densities where is viable. Our main technical result provides sufficient conditions on maximum degrees uniform hypergraph H guarantee edges, induced by binomial...

We develop new methods for the estimation of time-varying risk-neutral jump tails in asset returns. In contrast to existing procedures based on tightly parameterized models, our approach imposes much fewer structural assumptions, relying on extreme-value theory approximations together with short-maturity options. The new estimation approach explicitly allows the parameters characterizing the sh...

Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving …nancial data. We derive explicit …nite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium ...

In 2000, my wife Lynn and I were in Namibia researching the social organization of Elephantulus intufi (Rathbun and Rathbun 2006). During a meal at our study site which we shared with the landowner, his two sons and two archaeologists studying local rock art, the archaeologists showed us a newly published book (LewisWilliams 2000). When Justin Holloway, the youngest son of the landowner, saw th...