Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission

The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of $10^{-15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.Comment: 12 pages, 4 figures, to be published in Phys. Rev.

Potential of the next generation VHE instruments to probe the EBL (I): the low- and mid-VHE

The diffuse meta-galactic radiation field at ultraviolet to infrared wavelengths - commonly labeled extragalactic background light (EBL) - contains the integrated emission history of the universe. Difficult to access via direct observations indirect constraints on its density can be derived through observations of very-high energy (VHE; E>100 GeV) gamma-rays from distant sources: the VHE photons are attenuated via pair-production with the low energy photons from the EBL, leaving a distinct imprint in the VHE spectra measured on earth. Discoveries made with current generation VHE observatories like H.E.S.S. and MAGIC enabled strong constraints on the density of the EBL especially in the near-infrared. In this article the prospect of future VHE observatories to derive new constraints on the EBL density are discussed. To this end, results from current generation instruments will be extrapolated to the future experiment's sensitivity and investigated for their power to enable new methods and improved constraints on the EBL density.Comment: Accepted for publication in Astroparticle Physics; v2: extended discussion following referees comments, conclusions unchange

Improving likelihood-based inference in control rate regression

Control rate regression is a diffuse approach to account for heterogeneity among studies in meta-analysis by including information about the outcome risk of patients in the control condition. Correcting for the presence of measurement error affecting risk information in the treated and in the control group has been recognized as a necessary step to derive reliable inferential conclusions. Within this framework, the paper considers the problem of small sample size as an additional source of misleading inference about the slope of the control rate regression. Likelihood procedures relying on first-order approximations are shown to be substantially inaccurate, especially when dealing with increasing heterogeneity and correlated measurement errors. We suggest to address the problem by relying on higher-order asymptotics. In particular, we derive Skovgaard's statistic as an instrument to improve the accuracy of the approximation of the signed profile log-likelihood ratio statistic to the standard normal distribution. The proposal is shown to provide much more accurate results than standard likelihood solutions, with no appreciable computational effort. The advantages of Skovgaard's statistic in control rate regression are shown in a series of simulation experiments and illustrated in a real data example. R code for applying first- and second-order statistic for inference on the slope on the control rate regression is provided

Systematic errors and combination of individual CRF solutions in the framework of the international pilot project for the next ICRF

A new international Pilot Project for the re-determination of the ICRF was initiated by the International VLBI Service for Geodesy and Astrometry (IVS) in January 2005. The purpose of this project is to compare the individual CRF solutions and to analyze their systematic and random errors with focus on the selection of the optimal strategy for the next ICRF realization. Eight radio source catalogues provided by the IVS Analysis Centers GA, SHAO, DGFI, GIUB-BKG, JPL, MAO NANU, GSFC, USNO were analyzed. In present study, four analytical models were used to investigate the systematic differences between solutions: solid rotation, rotation and deformation (IERS method), and expansion in orthogonal functions: Legendre-Fourier polynomials and spherical functions. It was found that expansions by orthogonal function describe the differences between individual catalogues better than the two former models. Finally, the combined CRF was generated. Using the radio source positions from this combined catalogue for estimation of EOP has shown improvement of the uncertainty of the celestial pole offset time series.Comment: 9 pages, 8 figures. Presented at the XXVIth IAU General Assembly, JD16, Prague, Czech Republic, 14-25 August 200

High-cadence spectroscopy of M-dwarfs – II. Searching for stellar pulsations with HARPS

Stellar oscillations appear all across the Hertzsprung–Russell diagram. Recent theoretical studies support their existence also in the atmosphere of M dwarfs. These studies predict for them short periodicities ranging from 20 min to 3 h. Our Cool Tiny Beats (CTB) programme aims at finding these oscillations for the very first time. With this goal, CTB explores the short time domain of M dwarfs using radial velocity data from the High Accuracy Radial velocity Planet Searcher (HARPS)-European Southern Observatory and HARPS-N high-precision spectrographs. Here we present the results for the two most long-term stable targets observed to date with CTB, GJ 588 and GJ 699 (i.e. Barnard's star). In the first part of this work we detail the correction of several instrumental effects. These corrections are especially relevant when searching for subnight signals. Results show no significant signals in the range where M dwarfs pulsations were predicted. However, we estimate that stellar pulsations with amplitudes larger than ∼0.5 m s−1 can be detected with a 90 per cent completeness with our observations. This result, along with the excess of power regions detected in the periodograms, opens the possibility of non-resolved very low amplitude pulsation signals. Next generation more precise instrumentation would be required to detect such oscillations. However, the possibility of detecting pulsating M-dwarf stars with larger amplitudes is feasible due to the short size of the analysed sample. This motivates the need for completeness of the CTB survey