Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models

Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only $O(d^3n^{-3/2})$, where $d$ is the number of parameters and $n$ the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models.Comment: Published in at http://dx.doi.org/10.1214/07-AOS512 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

HD 174884: a strongly eccentric, short-period early-type binary system discovered by CoRoT

Accurate photometric CoRoT space observations of a secondary seismological target, HD 174884, led to the discovery that this star is an astrophysically important double-lined eclipsing spectroscopic binary in an eccentric orbit (e of about 0.3), unusual for its short (3.65705d) orbital period. The high eccentricity, coupled with the orientation of the binary orbit in space, explains the very unusual observed light curve with strongly unequal primary and secondary eclipses having the depth ratio of 1-to-100 in the CoRoT 'seismo' passband. Without the high accuracy of the CoRoT photometry, the secondary eclipse, 1.5 mmag deep, would have gone unnoticed. A spectroscopic follow-up program provided 45 high dispersion spectra. The analysis of the CoRoT light curve was performed with an adapted version of PHOEBE that supports CoRoT passbands. The final solution was obtained by simultaneous fitting of the light and the radial velocity curves. Individual star spectra were derived by spectrum disentangling. The uncertainties of the fit were derived by bootstrap resampling and the solution uniqueness was tested by heuristic scanning. The results provide a consistent picture of the system composed of two late B stars. The Fourier analysis of the light curve fit residuals yields two components, with orbital frequency multiples and an amplitude of about 0.1 mmag, which are tentatively interpreted as tidally induced pulsations. An extensive comparison with theoretical models is carried out by means of the Levenberg-Marquardt minimization technique and the discrepancy between models and the derived parameters is discussed. The best fitting models yield a young system age of 125 million years which is consistent with the eccentric orbit and synchronous component rotation at periastron.Comment: 15 pages, 12 figures. Accepted for publication by A&

Observational evidence for a metal rich atmosphere on the super-Earth GJ1214b

We report observations of two consecutive transits of the warm super-Earth exoplanet GJ1214b at 3.6 and 4.5 microns with the Infrared Array Camera instrument on-board the Spitzer Space Telescope. The two transit light curves allow for the determination of the transit parameters for this system. We find these paremeters to be consistent with the previously determined values and no evidence for transit timing variations. The main investigation consists of measuring the transit depths in each bandpass to constrain the planet's transmission spectrum. Fixing the system scale and impact parameters, we measure R_p/R_star=0.1176 (+0.0008/-0.0009) and 0.1163 (+0.0010/-0.0008) at 3.6 and 4.5 microns, respectively. Combining these data with the previously reported MEarth Observatory measurements in the red optical yields constraints on the GJ1214b's transmission spectrum and allows us to rule-out a cloud-free, solar composition (i.e., hydrogen-dominated) atmosphere at 4.5 sigma confidence. This independently confirms a recent finding that was based on a measurement of the planet's transmission spectrum using the VLT. The Spitzer, MEarth, and VLT observations together yield a remarkably flat transmission spectrum over the large wavelength domain spanned by the data. Consequently, cloud-free atmospheric models require more than 30% metals (assumed to be in the form of H2O by volume to be consistent with all the observations.Comment: Accepted for publication in ApJL. 13 pages, 3 figures, 1 tabl