Neutrino Flavor Ratio on Earth and at Astrophysical Sources

We present the reconstruction of neutrino flavor ratios at astrophysical sources. For distinguishing the pion source and the muon-damped source to the 3$\sigma$ level, the neutrino flux ratios, $R\equiv\phi(\nu_\mu)/(\phi(\nu_e)+\phi(\nu_\tau))$ and $S\equiv\phi(\nu_e)/\phi(\nu_\tau)$, need to be measured in accuracies better than 10%.Comment: 3 pages, 8 figures. Talk presented by T.C. Liu in ERICE 2009, Sicily

New n\sqrt{n}-consistent, numerically stable higher-order influence function estimators

Higher-Order Influence Functions (HOIFs) provide a unified theory for constructing rate-optimal estimators for a large class of low-dimensional (smooth) statistical functionals/parameters (and sometimes even infinite-dimensional functions) that arise in substantive fields including epidemiology, economics, and the social sciences. Since the introduction of HOIFs by Robins et al. (2008), they have been viewed mostly as a theoretical benchmark rather than a useful tool for statistical practice. Works aimed to flip the script are scant, but a few recent papers Liu et al. (2017, 2021b) make some partial progress. In this paper, we take a fresh attempt at achieving this goal by constructing new, numerically stable HOIF estimators (or sHOIF estimators for short with ``s'' standing for ``stable'') with provable statistical, numerical, and computational guarantees. This new class of sHOIF estimators (up to the 2nd order) was foreshadowed in synthetic experiments conducted by Liu et al. (2020a)

Risk Spillovers in Oil-Related CDS, Stock and Credit Markets

This paper examines risk transmission and migration among six US measures of credit and market risk during the full period 2004-2011 period and the 2009-2011 recovery subperiod, with a focus on four sectors related to the highly volatile oil price. There are more long-run equilibrium risk relationships and short-run causal relationships among the four oil-related Credit Default Swaps (CDS) indexes, the (expected equity volatility) VIX index and the (swaption expected volatility) SMOVE index for the full period than for the recovery subperiod. The auto sector CDS spread is the most error-correcting in the long run and also leads in the risk discovery process in the short run. On the other hand, the CDS spread of the highly regulated, natural monopoly utility sector does not error correct. The four oil-related CDS spread indexes are responsive to VIX in the short- and long-run, while no index is sensitive to SMOVE which, in turn, unilaterally assembles risk migration from VIX. The 2007-2008 Great Recession seems to have led to “localization” and less migration of credit and market risk in the oil-related sectors.Risk; Sectoral CDS; VIX; SMOVE; MOVE; Adjustments

Risk Spillovers in Oil-Related CDS, Stock and Credit Markets

This paper examines risk transmission and migration among six US measures of credit and market risk during the full period 2004-2011 period and the 2009-2011 recovery subperiod, with a focus on four sectors related to the highly volatile oil price. There are more long-run equilibrium risk relationships and short-run causal relationships among the four oil-related Credit Default Swaps (CDS) indexes, the (expected equity volatility) VIX index and the (swaption expected volatility) SMOVE index for the full period than for the recovery subperiod. The auto sector CDS spread is the most error-correcting in the long run and also leads in the risk discovery process in the short run. On the other hand, the CDS spread of the highly regulated, natural monopoly utility sector does not error correct. The four oil-related CDS spread indexes are responsive to VIX in the short- and long-run, while no index is sensitive to SMOVE which, in turn, unilaterally assembles risk migration from VIX. The 2007-2008 Great Recession seems to have led to “localization” and less migration of credit and market risk in the oil-related sectors.Risk, Sectoral CDS, VIX, SMOVE, MOVE, Adjustments.