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2 results on '"Lycée Stanislas, Paris"'

1. Asymptotic distribution of least squares estimators for linear models with dependent errors : regular designs

Author

Sophie Dede, Emmanuel Caron, Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), École Centrale de Nantes (ECN), and Lycée Stanislas, Paris

Subjects
Statistics and Probability, Independent and identically distributed random variables, FOS: Computer and information sciences, Asymptotic distribution, Mathematics - Statistics Theory, Statistics Theory (math.ST), Statistics - Applications, 01 natural sciences, Least squares, spectral density, 62F12, 62J05, 62M10, 62M15, 010104 statistics & probability, short memory processes, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Linear regression, FOS: Mathematics, Applied mathematics, Applications (stat.AP), 0101 mathematics, Mathematics, Central limit theorem, [STAT.AP]Statistics [stat]/Applications [stat.AP], Covariance matrix, 010102 general mathematics, Probability (math.PR), Linear model, Estimator, least squares estimator, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], linear model, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract

In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan, who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and on the error process. We show that for a large class of designs, the asymptotic covariance matrix is as simple as the independent and identically distributed case. We then estimate the covariance matrix using an estimator of the spectral density whose consistency is proved under very mild conditions., Comment: 31 pages

Published
2017
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2. The two Titan stellar occultations of 14 November 2003

Author

M. Kidger, H. Lüdemann, B. Thomé, F. Bode, Daisuke Baba, C. Martinez, François Colas, C. Tegtmeier, D. Fiel, Jean Lecacheux, Takahiro Nagayama, M. Kretlow, P. Schoenau, T. Payet, Françoise Roques, S. Renner, Brian Fraser, Ian S. Glass, M. Rapaport, H. J. Bode, D. Neubauer, M. Hernandez, P. Meintjies, J. P. Teng, Robert R. Howell, C. Turk, S. Lacour, W. Beisker, F. Hund, C. Etienne, O. Naranjo, Bruno Sicardy, Tetsuya Nagata, Thomas Widemann, A. Bellucci, Terry J. Jones, Francesca Ferri, K.-L. Bath, E. Frappa, S. Itting-Enke, J. Lüdemann, A. Jansen, Agnes Fienga, Emmanuel Lellouch, A. Tegtmeier, G. Hesler, J. L. Ortiz, S. Pau, P. Rosenzweig, A. Peyrot, M. Vignand, C. DeWitt, Laboratoire d'études spatiales et d'instrumentation en astrophysique (LESIA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Pôle Astronomie du LESIA, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Ingénieurs, Techniciens et Administratifs, Pôle Planétologie du LESIA, Laboratoire d'études spatiales et d'instrumentation en astrophysique = Laboratory of Space Studies and Instrumentation in Astrophysics (LESIA), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Lille-Centre National de la Recherche Scientifique (CNRS), International Occultation Timing Association, European Section (IOTA/ES), Centro Interdipartimentale di Studi e Attività Spaziali 'Giuseppe Colombo', Università di Padova (CISAS), Observatoire de Paris, Université Paris sciences et lettres (PSL), Instituto Superior de Ciencias Astronómicas, South African Astronomical Observatory (SAAO), Department of Astrophysics, Nagoya University, Windhoek, Hakos Guestfarm, Astronomical Society of Southern Africa, Boyden Observatory, University of the Free State, Association des Utilisateurs de Détecteurs Electroniques (AUDE), Association des Utilisateurs de Détecteurs Electroniques, Lycée Stanislas, Paris, Astronef-Planétarium de Saint-Etienne, Observatoire astronomique des Makes, Association Réunionnaise pour l'Etude du Ciel Austral (ARECA), Wyoming InfraRed Observatory, Department of Physics and Astronomy, Instituto de Astrofísica de Canarias (IAC), Instituto de Astrofisica de Andalucia, CSIC (IAA), Universidad de Los Andes, Facultad de Ciencias, Departamento de Física, Grupo de Astrofísica Teórica, Observatoire aquitain des sciences de l'univers (OASU), and Université Sciences et Technologies - Bordeaux 1 (UB)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Atmospheric Science, Haze, Equator, Soil Science, Aquatic Science, Oceanography, Atmospheric sciences, Latitude, symbols.namesake, Altitude, Geochemistry and Petrology, Earth and Planetary Sciences (miscellaneous), Southern Hemisphere, Stratosphere, Earth-Surface Processes, Water Science and Technology, Ecology, Paleontology, Forestry, Light curve, Geophysics, Space and Planetary Science, [SDU]Sciences of the Universe [physics], symbols, Titan (rocket family), [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], Geology
Abstract

[1] We report the observation of two stellar occultations by Titan on 14 November 2003, using stations in the Indian Ocean, southern Africa, Spain, and northern and southern Americas. These occultations probed altitudes between ∼550 and 250 km (∼1 to 250 μbar) in Titan's upper stratosphere. The light curves reveal a sharp inversion layer near 515 ± 6 km altitude (1.5 μbar pressure level), where the temperature increases by 15 K in only 6 km. This layer is close to an inversion layer observed fourteen months later by the Huygens HASI instrument during the entry of the probe in Titan's atmosphere on 14 January 2005 [Fulchignoni et al., 2005]. Central flashes observed during the first occultation provide constraints on the zonal wind regime at 250 km, with a strong northern jet (∼200 m s -1 ) around the latitude 55°N, wind velocities of ∼150 m s -1 near the equator, and progressively weaker winds as more southern latitudes are probed. The haze distribution around Titan's limb at 250 km altitude is close to that predicted by the Global Circulation Model of Rannou et al. (2004) in the southern hemisphere, but a clearing north of 40°N is necessary to explain our data. This contrasts with Rannou et al.'s (2004) model, which predicts a very thick polar hood over Titan's northern polar regions. Simultaneous observations of the flashes at various wavelengths provide a dependence of τ ∝ λ -q , with q = 1.8 ± 0.5 between 0.51 and 2.2 μm for the tangential optical depth of the hazes at 250 km altitude.

Published
2006
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