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On Low-Dimensional Projections of High-Dimensional Distributions
Low-Dimensional Projections High-Dimensional Distributions
2011/7/19
Let $P$ be a probability distribution on $q$-dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension $d << q$, most $d$-dimensional projections of $P$ look like a sc...
Covariance Estimation for Distributions with 2+εMoments
Covariance Estimation Distributions 2+εMoments
2011/7/7
We study the minimal sample size N=N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, and with an arbitrary fix...
Combining Predictive Distributions
calibration coherent combination formula density forecast
2011/7/5
Predictive distributions need to be aggregated when probabilistic forecasts are merged, or when expert opinions expressed in terms of probability distributions are fused.
Subdiagonal and Almost Uniform Distributions
Subdiagonal distribution almost uniform distribution exchangeable random order
2009/4/29
A distribution (function) F on [0,1] with F(t) less or equal t for all t is called subdiagonal. The extreme subdiagonal distributions are identified as those whose distribution functions are almost su...