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

On the two types of steady hard X-ray states of GRS 1915+105

Using the data of 5 years of RXTE observations we investigate the X-ray spectral and timing properties of GRS 1915+105 during the hard steady states. According to the results of our simultaneous X-ray spectral and timing analysis the behavior the source during the hard steady states can be reduced to a couple of major distinct types. i) Type I states: The dominant hard component of the energy spectrum has characteristic quasi- exponential cut-off at 50-120 keV. The broad-band power density spectrum of the source shows significant high frequency noise component with a cut-off at 60-80 Hz. ii) Type II states: The hard spectral component has a break in its slope at ~12-20 keV. The high frequency part of the power density spectrum fades quickly lacking significant variability at frequencies higher than ~30 Hz. These two types of the X-ray hard states are also clearly distinguished by their properties in the radio band: while during the type I observations the source tends to be 'radio-quiet', the type II observations are characterized by high level of radio flux ('plateau' radio states). In this work we demonstrate aforementioned differences using the data of 12 representative hard steady state observations. We conclude that the difference between these two types can be probably explained in terms of different structure of the accretion flow in the immediate vicinity of the compact object due to presence of relativistic outflow of matter.Comment: 16 pages, including 3 figures, submitted to Astrophysical Journal Letter