873 research outputs found
Two-Sample Testing in High Dimension and a Smooth Block Bootstrap for Time Series
This document contains three sections. The first two present new methods for two-sample testing where there are many variables of interest and the third presents a new methodology for time series bootstrapping.
In the first section we develop a test statistic for testing the equality of two population mean vectors in the "large-p-small-n" setting. Such a test must surmount the rank-deficiency of the sample covariance matrix, which breaks down the classic Hotelling T^(2) test. The proposed procedure, called the generalized component test, avoids full estimation of the covariance matrix by assuming that the p components admit a logical ordering such that the dependence between components is related to their displacement. The test is shown to be competitive with other recently developed methods under ARMA and long-range dependence structures and to achieve superior power for heavy-tailed data. The test does not assume equality of covariance matrices between the two populations, is robust to heteroscedasticity in the component variances, and requires very little computation time, which allows its use in settings with very large p. An analysis of mitochondrial calcium concentration in mouse cardiac muscles over time and of copy number variations in a glioblastoma multiforme data set from The Cancer Genome Atlas are carried out to illustrate the test.
In the second section we present a theorem establishing a power improvement to the Benjamini-Hochberg procedure for controlling the false discovery rate when it is applied to test statistics which have been adjusted for the effects of latent factors. We extend recently published methodology to the context of serially dependent test statistics by presenting a frequency-domain adaptation of their procedure. We show that our harmonic factor adjustment to the test statistics improves the power of the Benjamini-Hochberg procedure without compromising its control of the false discovery rate when the test statistics are affected by latent periodic components. An illustration of our methodology is given in an analysis of copy number variations, which are measured along a chromosome and tend to exhibit serial dependence; power gains from our harmonic factor adjustment are demonstrated.
In the third section we present a smoothed bootstrap procedure for time series data. Unlike with independent data, smoothed boostraps have received little consideration for time series. However, as evidenced in the iid smooth bootstrap, additional data smoothing steps within resampling can improve bootstrap approximations of the distributions of statistics, especially when such sampling distributions depend critically on unknown and smooth (e.g., infinite-dimensional) population quantities, such as marginal densities. To broaden the effectiveness of the bootstrap for time series, we propose a smooth bootstrap based on modifying a state-of-the-art block resampling approach for dependent data based on tapering windows. The resulting smooth (extended) tapered block bootstrap
(TBB) is shown to provide valid variance and distributional approximations over a broad class of parameters and statistics for stationary time series, formulated in terms of statistical functionals (e.g., smooth function model statistics, L- and M-estimators, rank statistics). Our treatment goes beyond statistics as smooth functions of sample averages, showing that the smooth TBB has applicability in inference cases which have not been formally established for other TBB versions. Some finite-sample simulations also provide evidence that smoothing steps enhance the performance of the block bootstrap for various statistical functionals
The Fifth Data Release of the Sloan Digital Sky Survey
This paper describes the Fifth Data Release (DR5) of the Sloan Digital Sky
Survey (SDSS). DR5 includes all survey quality data taken through June 2005 and
represents the completion of the SDSS-I project (whose successor, SDSS-II will
continue through mid-2008). It includes five-band photometric data for 217
million objects selected over 8000 square degrees, and 1,048,960 spectra of
galaxies, quasars, and stars selected from 5713 square degrees of that imaging
data. These numbers represent a roughly 20% increment over those of the Fourth
Data Release; all the data from previous data releases are included in the
present release. In addition to "standard" SDSS observations, DR5 includes
repeat scans of the southern equatorial stripe, imaging scans across M31 and
the core of the Perseus cluster of galaxies, and the first spectroscopic data
from SEGUE, a survey to explore the kinematics and chemical evolution of the
Galaxy. The catalog database incorporates several new features, including
photometric redshifts of galaxies, tables of matched objects in overlap regions
of the imaging survey, and tools that allow precise computations of survey
geometry for statistical investigations.Comment: ApJ Supp, in press, October 2007. This paper describes DR5. The SDSS
Sixth Data Release (DR6) is now public, available from http://www.sdss.or
The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe
The preponderance of matter over antimatter in the early Universe, the
dynamics of the supernova bursts that produced the heavy elements necessary for
life and whether protons eventually decay --- these mysteries at the forefront
of particle physics and astrophysics are key to understanding the early
evolution of our Universe, its current state and its eventual fate. The
Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed
plan for a world-class experiment dedicated to addressing these questions. LBNE
is conceived around three central components: (1) a new, high-intensity
neutrino source generated from a megawatt-class proton accelerator at Fermi
National Accelerator Laboratory, (2) a near neutrino detector just downstream
of the source, and (3) a massive liquid argon time-projection chamber deployed
as a far detector deep underground at the Sanford Underground Research
Facility. This facility, located at the site of the former Homestake Mine in
Lead, South Dakota, is approximately 1,300 km from the neutrino source at
Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino
charge-parity symmetry violation and mass ordering effects. This ambitious yet
cost-effective design incorporates scalability and flexibility and can
accommodate a variety of upgrades and contributions. With its exceptional
combination of experimental configuration, technical capabilities, and
potential for transformative discoveries, LBNE promises to be a vital facility
for the field of particle physics worldwide, providing physicists from around
the globe with opportunities to collaborate in a twenty to thirty year program
of exciting science. In this document we provide a comprehensive overview of
LBNE's scientific objectives, its place in the landscape of neutrino physics
worldwide, the technologies it will incorporate and the capabilities it will
possess.Comment: Major update of previous version. This is the reference document for
LBNE science program and current status. Chapters 1, 3, and 9 provide a
comprehensive overview of LBNE's scientific objectives, its place in the
landscape of neutrino physics worldwide, the technologies it will incorporate
and the capabilities it will possess. 288 pages, 116 figure
Measurement of the cosmic ray spectrum above eV using inclined events detected with the Pierre Auger Observatory
A measurement of the cosmic-ray spectrum for energies exceeding
eV is presented, which is based on the analysis of showers
with zenith angles greater than detected with the Pierre Auger
Observatory between 1 January 2004 and 31 December 2013. The measured spectrum
confirms a flux suppression at the highest energies. Above
eV, the "ankle", the flux can be described by a power law with
index followed by
a smooth suppression region. For the energy () at which the
spectral flux has fallen to one-half of its extrapolated value in the absence
of suppression, we find
eV.Comment: Replaced with published version. Added journal reference and DO
Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory
The Auger Engineering Radio Array (AERA) is part of the Pierre Auger
Observatory and is used to detect the radio emission of cosmic-ray air showers.
These observations are compared to the data of the surface detector stations of
the Observatory, which provide well-calibrated information on the cosmic-ray
energies and arrival directions. The response of the radio stations in the 30
to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of
the incoming electric field. For the latter, the energy deposit per area is
determined from the radio pulses at each observer position and is interpolated
using a two-dimensional function that takes into account signal asymmetries due
to interference between the geomagnetic and charge-excess emission components.
The spatial integral over the signal distribution gives a direct measurement of
the energy transferred from the primary cosmic ray into radio emission in the
AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air
shower arriving perpendicularly to the geomagnetic field. This radiation energy
-- corrected for geometrical effects -- is used as a cosmic-ray energy
estimator. Performing an absolute energy calibration against the
surface-detector information, we observe that this radio-energy estimator
scales quadratically with the cosmic-ray energy as expected for coherent
emission. We find an energy resolution of the radio reconstruction of 22% for
the data set and 17% for a high-quality subset containing only events with at
least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO
Search for gravitational wave bursts in LIGO's third science run
We report on a search for gravitational wave bursts in data from the three
LIGO interferometric detectors during their third science run. The search
targets subsecond bursts in the frequency range 100-1100 Hz for which no
waveform model is assumed, and has a sensitivity in terms of the
root-sum-square (rss) strain amplitude of hrss ~ 10^{-20} / sqrt(Hz). No
gravitational wave signals were detected in the 8 days of analyzed data.Comment: 12 pages, 6 figures. Amaldi-6 conference proceedings to be published
in Classical and Quantum Gravit
Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy
We measure the energy emitted by extensive air showers in the form of radio
emission in the frequency range from 30 to 80 MHz. Exploiting the accurate
energy scale of the Pierre Auger Observatory, we obtain a radiation energy of
15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV
arriving perpendicularly to a geomagnetic field of 0.24 G, scaling
quadratically with the cosmic-ray energy. A comparison with predictions from
state-of-the-art first-principle calculations shows agreement with our
measurement. The radiation energy provides direct access to the calorimetric
energy in the electromagnetic cascade of extensive air showers. Comparison with
our result thus allows the direct calibration of any cosmic-ray radio detector
against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI.
Supplemental material in the ancillary file
Quantum state preparation and macroscopic entanglement in gravitational-wave detectors
Long-baseline laser-interferometer gravitational-wave detectors are operating
at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within
a broad frequency band. Such a low classical noise budget has already allowed
the creation of a controlled 2.7 kg macroscopic oscillator with an effective
eigenfrequency of 150 Hz and an occupation number of 200. This result, along
with the prospect for further improvements, heralds the new possibility of
experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical
behavior of objects in the realm of everyday experience - using
gravitational-wave detectors. In this paper, we provide the mathematical
foundation for the first step of a MQM experiment: the preparation of a
macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum
state, which is possible if the interferometer's classical noise beats the SQL
in a broad frequency band. Our formalism, based on Wiener filtering, allows a
straightforward conversion from the classical noise budget of a laser
interferometer, in terms of noise spectra, into the strategy for quantum state
preparation, and the quality of the prepared state. Using this formalism, we
consider how Gaussian entanglement can be built among two macroscopic test
masses, and the performance of the planned Advanced LIGO interferometers in
quantum-state preparation
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