Brownian distance covariance

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with respect to a stochastic process is introduced, and it is shown that population distance covariance coincides with the covariance with respect to Brownian motion; thus, both can be called Brownian distance covariance. In the bivariate case, Brownian covariance is the natural extension of product-moment covariance, as we obtain Pearson product-moment covariance by replacing the Brownian motion in the definition with identity. The corresponding statistic has an elegantly simple computing formula. Advantages of applying Brownian covariance and correlation vs the classical Pearson covariance and correlation are discussed and illustrated.Comment: This paper discussed in: [arXiv:0912.3295], [arXiv:1010.0822], [arXiv:1010.0825], [arXiv:1010.0828], [arXiv:1010.0836], [arXiv:1010.0838], [arXiv:1010.0839]. Rejoinder at [arXiv:1010.0844]. Published in at http://dx.doi.org/10.1214/09-AOAS312 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A spectroscopic survey of Orion KL between 41.5 and 50 GHz

Orion KL is one of the most frequently observed sources in the Galaxy, and the site where many molecular species have been discovered for the first time. With the availability of powerful wideband backends, it is nowadays possible to complete spectral surveys in the entire mm-range to obtain a spectroscopically unbiased chemical picture of the region. In this paper we present a sensitive spectral survey of Orion KL, made with one of the 34m antennas of the Madrid Deep Space Communications Complex in Robledo de Chavela, Spain. The spectral range surveyed is from 41.5 to 50 GHz, with a frequency spacing of 180 kHz (equivalent to about 1.2 km/s, depending on the exact frequency). The rms achieved ranges from 8 to 12 mK. The spectrum is dominated by the J=1-0 SiO maser lines and by radio recombination lines (RRLs), which were detected up to Delta_n=11. Above a 3-sigma level, we identified 66 RRLs and 161 molecular lines corresponding to 39 isotopologues from 20 molecules; a total of 18 lines remain unidentified, two of them above a 5-sigma level. Results of radiative modelling of the detected molecular lines (excluding masers) are presented. At this frequency range, this is the most sensitive survey and also the one with the widest band. Although some complex molecules like CH_3CH_2CN and CH_2CHCN arise from the hot core, most of the detected molecules originate from the low temperature components in Orion KL.Comment: Accepted for Astronomy and Astrophysics. 29 pages, 5 tables, 6 figure

Financial Forces and the Future of American Higher Education

Recent shifts in state funding are altering the most basic realities of American higher education, from student access to faculty research

Resident and Nonresident Tuition and Enrollment at Flagship State Universities

[Excerpt] How tuition levels, or the availability of grant or loan aid, influence access are empirical questions that we will not address in this chapter. Rather, we will analyze how tuition and enrollment strategies at institutions react to changes in federal and state need-based student aid and to state appropriations to public higher education institutions. The former increases student mobility by expanding their choice set, while the latter does not travel with the student