Testing the goodness of fit of a hilbertian autoregressive model

The presented methodology for testing the goodness-of-fit of an Autoregressive Hilbertian model (ARH(1) model) provides an infinite-dimensional formulation of the approach proposed in Koul and Stute (1999), based on empirical process marked by residuals. Applying a central and functional central limit result for Hilbert-valued martingale difference sequences, the asymptotic behavior of the formulated H-valued empirical process, also indexed by H, is obtained under the null hypothesis. The limiting process is H-valued generalized (i.e., indexed by H) Wiener process, leading to an asymptotically distribution free test. Consistency is also analyzed. The case of misspecified autocorrelation operator of the ARH(1) process is addressed as well. Beyond the Euclidean setting, this approach allows to implement goodness of fit testing in the context of manifold and spherical functional autoregressive processes

Bandwidth selection for kernel density estimation with length-biased data

Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the context of length-biased data, proposing two consistent bootstrap methods that we use for bandwidth selection. Apart from the bootstrap bandwidth selectors we suggest a rule-of-thumb. These bandwidth selection proposals are compared with a least-squares cross-validation method. A simulation study is accomplished to understand the behaviour of the procedures in finite samples

Functional Covariate-Adjusted Partial Area under the Specificity-ROC Curve with an Application to Metabolic Syndrome Diagnosis

Due to recent advances in technology, medical diagnosis data are becoming increasingly complex and, nowadays, applications where measurements are curves or images are ubiquitous. Motivated by the need of modeling a functional covariate on a metabolic syndrome case study, we develop a nonparametric functional regression model for the area under the specificity receiver operating characteristic curve. This partial area is a meaningful summary measure of diagnostic accuracy for cases in which misdiagnosis of diseased subjects may lead to serious clinical consequences, and hence it is critical to maintain a high sensitivity. Its normalized value can be interpreted as the average specificity over the interval of sensitivities considered, thus summarizing the trade-off between sensitivity and specificity. Our methods are motivated by, and applied to, a metabolic syndrome study that investigates how restricting the sensitivity of the gamma-glutamyl-transferase, a metabolic syndrome marker, to certain clinical meaningful values, affects its corresponding specificity and how it might change for different curves of arterial oxygen saturation. Application of our methods suggests that oxygen saturation is key to gamma-glutamyl transferase’s performance and that some of the different intervals of sensitivities considered offer a good tradeoff between sensitivity and specificity. The simulation study shows that the estimator associated with our model is able to recover successfully the true overall shape of the functional covariate-adjusted partial area under the curve in different complex scenariosPartially funded by Fondecyt Grants 11130541 (first author) and 11121186 (second author). Supported in part by the Spanish Ministry of Science and Innovation through project MTM2008-03010S

Exploring wind direction and SO2 concentration by circular-linear density estimation

The study of environmental problems usually requires the description of variables with different nature and the assessment of relations between them. In this work, an algorithm for flexible estimation of the joint density for a circular-linear variable is proposed. The method is applied for exploring the relation between wind direction and SO2 concentration in a monitoring station close to a power plant located in Galicia (NW-Spain), in order to compare the effectiveness of precautionary measures for pollutants reduction in two different years.Comment: 17 pages, 7 figures, 2 table

<i>Gaia</i> Data Release 1. Summary of the astrometric, photometric, and survey properties

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the HIPPARCOS and Tycho-2 catalogues – a realisation of the Tycho-Gaia Astrometric Solution (TGAS) – and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR-Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr−1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 HIPPARCOS stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr−1. For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data

Gaia Data Release 1: Testing parallaxes with local Cepheids and RR Lyrae stars

Context. Parallaxes for 331 classical Cepheids, 31 Type II Cepheids, and 364 RR Lyrae stars in common between Gaia and the Hipparcos and Tycho-2 catalogues are published in Gaia Data Release 1 (DR1) as part of the Tycho-Gaia Astrometric Solution (TGAS). Aims. In order to test these first parallax measurements of the primary standard candles of the cosmological distance ladder, which involve astrometry collected by Gaia during the initial 14 months of science operation, we compared them with literature estimates and derived new period-luminosity (PL), period-Wesenheit (PW) relations for classical and Type II Cepheids and infrared PL, PL-metallicity (PLZ), and optical luminosity-metallicity (M V -[Fe/H]) relations for the RR Lyrae stars, with zero points based on TGAS. Methods. Classical Cepheids were carefully selected in order to discard known or suspected binary systems. The final sample comprises 102 fundamental mode pulsators with periods ranging from 1.68 to 51.66 days (of which 33 with σ Ω /Ω < 0.5). The Type II Cepheids include a total of 26 W Virginis and BL Herculis stars spanning the period range from 1.16 to 30.00 days (of which only 7 with σ Ω /Ω < 0.5). The RR Lyrae stars include 200 sources with pulsation period ranging from 0.27 to 0.80 days (of which 112 with σ Ω /Ω < 0.5). The new relations were computed using multi-band (V,I,J,K s ) photometry and spectroscopic metal abundances available in the literature, and by applying three alternative approaches: (i) linear least-squares fitting of the absolute magnitudes inferred from direct transformation of the TGAS parallaxes; (ii) adopting astrometry-based luminosities; and (iii) using a Bayesian fitting approach. The last two methods work in parallax space where parallaxes are used directly, thus maintaining symmetrical errors and allowing negative parallaxes to be used. The TGAS-based PL,PW,PLZ, and M V - [Fe/H] relations are discussed by comparing the distance to the Large Magellanic Cloud provided by different types of pulsating stars and alternative fitting methods. Results. Good agreement is found from direct comparison of the parallaxes of RR Lyrae stars for which both TGAS and HST measurements are available. Similarly, very good agreement is found between the TGAS values and the parallaxes inferred from the absolute magnitudes of Cepheids and RR Lyrae stars analysed with the Baade-Wesselink method. TGAS values also compare favourably with the parallaxes inferred by theoretical model fitting of the multi-band light curves for two of the three classical Cepheids and one RR Lyrae star, which were analysed with this technique in our samples. The K-band PL relations show the significant improvement of the TGAS parallaxes for Cepheids and RR Lyrae stars with respect to the Hipparcos measurements. This is particularly true for the RR Lyrae stars for which improvement in quality and statistics is impressive. Conclusions. TGAS parallaxes bring a significant added value to the previous Hipparcos estimates. The relations presented in this paper represent the first Gaia-calibrated relations and form a work-in-progress milestone report in the wait for Gaia-only parallaxes of which a first solution will become available with Gaia Data Release 2 (DR2) in 2018. © ESO, 2017

Gaia Early Data Release 3 Acceleration of the Solar System from Gaia astrometry

Context. Gaia Early Data Release 3 (Gaia EDR3) provides accurate astrometry for about 1.6 million compact (QSO-like) extragalactic sources, 1.2 million of which have the best-quality five-parameter astrometric solutions. Aims. The proper motions of QSO-like sources are used to reveal a systematic pattern due to the acceleration of the solar systembarycentre with respect to the rest frame of the Universe. Apart from being an important scientific result by itself, the acceleration measured in this way is a good quality indicator of the Gaia astrometric solution. Methods. Theeffect of the acceleration was obtained as a part of the general expansion of the vector field of proper motions in vector spherical harmonics (VSH). Various versions of the VSH fit and various subsets of the sources were tried and compared to get the most consistent result and a realistic estimate of its uncertainty. Additional tests with the Gaia astrometric solution were used to get a better idea of the possible systematic errors in the estimate. Results. Our best estimate of the acceleration based on Gaia EDR3 is (2.32 +/- 0.16) x 10(-10) m s(-2) (or 7.33 +/- 0.51 km s(-1) Myr-1) towards alpha = 269.1 degrees +/- 5.4 degrees, delta = -31.6 degrees +/- 4.1 degrees, corresponding to a proper motion amplitude of 5.05 +/- 0.35 mu as yr(-1). This is in good agreement with the acceleration expected from current models of the Galactic gravitational potential. We expect that future Gaia data releases will provide estimates of the acceleration with uncertainties substantially below 0.1 mu as yr(-1).Peer reviewe

Gaia Focused Product Release: Radial velocity time series of long-period variables

The third Gaia Data Release (DR3) provided photometric time series of more than 2 million long-period variable (LPV) candidates. Anticipating the publication of full radial-velocity (RV) in DR4, this Focused Product Release (FPR) provides RV time series for a selection of LPVs with high-quality observations. We describe the production and content of the Gaia catalog of LPV RV time series, and the methods used to compute variability parameters published in the Gaia FPR. Starting from the DR3 LPVs catalog, we applied filters to construct a sample of sources with high-quality RV measurements. We modeled their RV and photometric time series to derive their periods and amplitudes, and further refined the sample by requiring compatibility between the RV period and at least one of the $G$, $G_{\rm BP}$, or $G_{\rm RP}$ photometric periods. The catalog includes RV time series and variability parameters for 9\,614 sources in the magnitude range $6\lesssim G/{\rm mag}\lesssim 14$, including a flagged top-quality subsample of 6\,093 stars whose RV periods are fully compatible with the values derived from the $G$, $G_{\rm BP}$, and $G_{\rm RP}$ photometric time series. The RV time series contain a mean of 24 measurements per source taken unevenly over a duration of about three years. We identify the great most sources (88%) as genuine LPVs, with about half of them showing a pulsation period and the other half displaying a long secondary period. The remaining 12% consists of candidate ellipsoidal binaries. Quality checks against RVs available in the literature show excellent agreement. We provide illustrative examples and cautionary remarks. The publication of RV time series for almost 10\,000 LPVs constitutes, by far, the largest such database available to date in the literature. The availability of simultaneous photometric measurements gives a unique added value to the Gaia catalog (abridged)Comment: 36 pages, 38 figure