### "Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical Models" (Next Week at the Statistics Seminar)

*Attention conservation notice:* Publicity for an upcoming
academic talk, of interest only if (1) you care about quantifying uncertainty
in statistics, and (2) will be in Pittsburgh on Monday.
I am late in publicizing this, but hope it will help drum up attendance
anyway:

- Mladen Kolar, "Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical Models"
*Abstract:* Undirected graphical models are used extensively in the
biological and social sciences to encode a pattern of conditional independences
between variables, where the absence of an edge between two nodes $a$ and $b$
indicates that the corresponding two variables $X_a$ and $X_b$ are believed to
be conditionally independent, after controlling for all other measured
variables. In the Gaussian case, conditional independence corresponds to a
zero entry in the precision matrix $\Omega$ (the inverse of the covariance
matrix $\Sigma$). Real data often exhibits heavy tail dependence between
variables, which cannot be captured by the commonly-used Gaussian or
nonparanormal (Gaussian copula) graphical models. In this paper, we study the
transelliptical model, an elliptical copula model that generalizes Gaussian and
nonparanormal models to a broader family of distributions. We propose the
ROCKET method, which constructs an estimator of $\Omega_{ab}$ that we prove to
be asymptotically normal under mild assumptions. Empirically, ROCKET
outperforms the nonparanormal and Gaussian models in terms of achieving
accurate inference on simulated data. We also compare the three methods on
real data (daily stock returns), and find that the ROCKET estimator is the only
method whose behavior across subsamples agrees with the distribution predicted
by the theory. (Joint work with Rina Foygel Barber.)
*Time and place:* 4--5 pm on Monday, 28 September 2015, in Doherty Hall 1112.

As always, the talk is free and open to the public.

Enigmas of Chance

Posted at September 26, 2015 23:58 | permanent link