8,515 research outputs found

### Inference on Treatment Effects After Selection Amongst High-Dimensional Controls

We propose robust methods for inference on the effect of a treatment variable
on a scalar outcome in the presence of very many controls. Our setting is a
partially linear model with possibly non-Gaussian and heteroscedastic
disturbances. Our analysis allows the number of controls to be much larger than
the sample size. To make informative inference feasible, we require the model
to be approximately sparse; that is, we require that the effect of confounding
factors can be controlled for up to a small approximation error by conditioning
on a relatively small number of controls whose identities are unknown. The
latter condition makes it possible to estimate the treatment effect by
selecting approximately the right set of controls. We develop a novel
estimation and uniformly valid inference method for the treatment effect in
this setting, called the "post-double-selection" method. Our results apply to
Lasso-type methods used for covariate selection as well as to any other model
selection method that is able to find a sparse model with good approximation
properties.
The main attractive feature of our method is that it allows for imperfect
selection of the controls and provides confidence intervals that are valid
uniformly across a large class of models. In contrast, standard post-model
selection estimators fail to provide uniform inference even in simple cases
with a small, fixed number of controls. Thus our method resolves the problem of
uniform inference after model selection for a large, interesting class of
models. We illustrate the use of the developed methods with numerical
simulations and an application to the effect of abortion on crime rates

### Low Luminosity States of the Black Hole Candidate GX~339--4. II. Timing Analysis

Here we present timing analysis of a set of eight Rossi X-ray Timing Explorer
(RXTE) observations of the black hole candidate GX 339-4 that were taken during
its hard/low state. On long time scales, the RXTE All Sky Monitor data reveal
evidence of a 240 day periodicity, comparable to timescales expected from
warped, precessing accretion disks. On short timescales all observations save
one show evidence of a persistent f approximately equal to 0.3 Hz QPO. The
broad band (10^{-3}-10^2 Hz) power appears to be dominated by two independent
processes that can be modeled as very broad Lorentzians with Q approximately
less than 1. The coherence function between soft and hard photon variability
shows that if these are truly independent processes, then they are individually
coherent, but they are incoherent with one another. This is evidenced by the
fact that the coherence function between the hard and soft variability is near
unity between 0.005-10 Hz but shows evidence of a dip at f approximately equal
to 1 Hz. This is the region of overlap between the broad Lorentzian fits to the
PSD. Similar to Cyg X-1, the coherence also drops dramatically at frequencies
approximately greater than 10 Hz. Also similar to Cyg X-1, the hard photon
variability is seen to lag the soft photon variability with the lag time
increasing with decreasing Fourier frequency. The magnitude of this time lag
appears to be positively correlated with the flux of GX 339-4. We discuss all
of these observations in light of current theoretical models of both black hole
spectra and temporal variability.Comment: To Appear in the AStrophysical Journa

### A Lensed Arc in the Low Redshift Cluster Abell 2124

We report the discovery of an arc-like object 27" from the center of the cD
galaxy in the redshift $z=0.066$ cluster A2124. Observations with the Keck II
telescope reveal that the object is a background galaxy at $z=0.573$,
apparently lensed into an arc of length \sim 8 \farcs5 and total R magnitude
$m_R = 20.86\pm0.07$. The width of the arc is resolved; we estimate it to be
$\sim$0\farcs6 after correcting for seeing. A lens model of the A2124 core mass
distribution consistent with the cluster galaxy velocity dispersion reproduces
the observed arc geometry and indicates a magnification factor \gta 9. With
this magnification, the strength of the [OII] \lambda 3727 line implies a
star-formation rate of SFR \sim 0.4 h^{-2}\msun yr^{-1}$. A2124 thus appears to
be the lowest redshift cluster known to exhibit strong lensing of a distant
background galaxy.Comment: 6 pages using emulateapj.sty; 4 Postscript figures; Figure 4 uses
color. Accepted for publication, but ApJ Letters' new policy of counting data
images makes the manuscript too long; will appear in main journal. This final
version has minor correction

### A Unified Description of the Timing Features of Accreting X-ray Binaries

We study an empirical model for a unified description of the power spectra of
accreting neutron stars and black holes. This description is based on a
superposition of multiple Lorentzians and offers the advantage that all QPO and
noise components are dealt with in the same way, without the need of deciding
in advance the nature of each component. This approach also allows us to
compare frequencies of features with high and low coherences in a consistent
manner and greatly facilitates comparison of power spectra across a wide range
of source types and states. We apply the model to six sources, the
low-luminosity X-ray bursters 1E 1724-3045, SLX 1735-269 and GS 1826-24, the
high-latitude transient XTE J1118+480, the bright system Cir X-1, and the Z
source GX 17+2. We find that it provides a good description of the observed
spectra, without the need for a scale-free (1/f) component. We update
previously reported correlations between characteristic frequencies of timing
features in the light of this new approach and discuss similarities between
different types of systems which may point towards similar underlying physics.Comment: 13 pages, to appear in The Astrophysical Journa

### Pivotal estimation in high-dimensional regression via linear programming

We propose a new method of estimation in high-dimensional linear regression
model. It allows for very weak distributional assumptions including
heteroscedasticity, and does not require the knowledge of the variance of
random errors. The method is based on linear programming only, so that its
numerical implementation is faster than for previously known techniques using
conic programs, and it allows one to deal with higher dimensional models. We
provide upper bounds for estimation and prediction errors of the proposed
estimator showing that it achieves the same rate as in the more restrictive
situation of fixed design and i.i.d. Gaussian errors with known variance.
Following Gautier and Tsybakov (2011), we obtain the results under weaker
sensitivity assumptions than the restricted eigenvalue or assimilated
conditions

### On the interpretation of the multicolour disc model for black hole candidates

We present a critical analysis of the usual interpretation of the multicolour
disc model parameters for black hole candidates in terms of the inner radius
and temperature of the accretion disc. Using a self-consistent model for the
radiative transfer and the vertical temperature structure in a Shakura-Sunyaev
disc, we simulate the observed disc spectra, taking into account doppler
blurring and gravitational redshift, and fit them with multicolour models. We
show not only that such a model systematically underestimates the value of the
inner disc radius, but that when the accretion rate and/or the energy
dissipated in the corona are allowed to change the inner edge of the disc, as
inferred from the multicolour model, appears to move even when it is in fact
fixed at the innermost stable orbit.Comment: 4 pages including 2 figures, accepted for publication in MNRA

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