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

The Physics of Disk Winds, Jets,and X-ray Variability in GRS 1915+105

We present new insights about accretion and ejection physics based on joint RXTE/Chandra HETGS studies of rapid X-ray variability in GRS 1915+105. For the first time, with fast phase-resolved spectroscopy of the rho state, we are able to show that changes in the broadband X-ray spectrum (RXTE) on timescales of seconds are associated with measurable changes in absorption lines (Chandra HETGS) from the accretion disk wind. Additionally, we make a direct detection of material evaporating from the radiation-pressure-dominated inner disk. Our X-ray data thus reveal the black hole as it ejects a portion of the inner accretion flow and then drives a wind from the outer disk, all in a bizarre cycle that lasts fewer than 60 seconds but can repeat for weeks. We find that the accretion disk wind may be sufficiently massive to play an active role in GRS 1915+105, not only in quenching the jet on long timescales, but also in possibly producing or facilitating transitions between classes of X-ray variability.Comment: 3 pages, 1 Figure. Proceedings of IAU Symposium 275 (Jets at all Scales), Buenos Aires, 13-17.09.2010; eds. G. Romero, R. Sunyaev, T. Bellon

Is 4U 0114+65 an eclipsing HMXB?

We present the pulsation and spectral characteristics of the HMXB 4U 0114+65 during a \emph{Suzaku} observation covering the part of the orbit that included the previously known low intensity emission of the source (dip) and the egress from this state. This dip has been interpreted in previous works as an X-ray eclipse. Notably, in this Suzaku observation, the count rate during and outside the dip vary by a factor of only 2-4 at odds with the eclipses of other HMXBs, where the intensity drops upto two orders of magnitude. The orbital intensity profile of 4U 0114+65 is characterized by a narrow dip in the RXTE-ASM (2-12 \rm{keV}) light curve and a shallower one in the Swift-BAT (15-50 \rm{keV}), which is different from eclipse ingress/egress behaviour of other HMXBs. The time-resolved spectral analysis reveal moderate absorption column density (N$_{H}$ - 2-20 $\times$ $10^{22}$ atoms $cm^{-2}$) and a relatively low equivalent width ($\sim$ 30 \rm{eV} \& 12 \rm{eV} of the iron K$_\alpha$ and K$_\beta$ lines respectively) as opposed to the typical X-ray spectra of HMXBs during eclipse where the equivalent width is $\sim$ 1 \rm{keV}. Both XIS and PIN data show clear pulsations during the dip, which we have further confirmed using the entire archival data of the IBIS/ISGRI and JEM-X instruments onboard \emph{INTEGRAL}. The results we presented question the previous interpretation of the dip in the light curve of 4U 0114+65 as an X-ray eclipse. We thus discuss alternative interpretations of the periodic dip in the light curve of 4U 0114+65.Comment: 16 pages, 7 figures, 1 table, Accepted in MNRA

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

Variability of X-ray binaries from an oscillating hot corona

The spectral and timing properties of an oscillating hot thermal corona are investigated. This oscillation is assumed to be due to a magneto-acoustic wave propagating within the corona and triggered by an external, non specified, excitation. A cylindrical geometry is adopted and, neglecting the rotation, the wave equation is solved in for different boundary conditions. The resulting X-ray luminosity, through thermal comptonization of embedded soft photons, is then computed, first analytically, assuming linear dependence between the local pressure disturbance and the radiative modulation. These calculations are also compared to Monte-Carlo simulations. The main results of this study are: (1) the corona plays the role of a low band-pass medium, its response to a white noise excitation being a at top noise Power Spectral Density (PSD) at low frequencies and a red noise at high frequency, (2) resonant peaks are present in the PSD. Their powers depend on the boundary conditions chosen and, more specifically, on the impedance adaptation with the external medium at the corona inner boundary. (3) The flat top noise level and break as well as the resonant peak frequencies are inversely proportional to the external radius rj. (4) Computed rms and f-spectra exhibit an overall increase of the variability with energy. Comparison with observed variability features, especially in the hard intermediate states of X-ray binaries are discussed.Comment: 12 pages, 7 figures, accepted for publication in MNRA

Multiwavelength Observations of GX 339-4 in 1996. II. Rapid X-ray Variability

As part of our multiwavelength campaign of GX 339-4 observations in 1996 we present the rapid X-ray variability observed July 26 using the RXTE when the source was in a hard state (= soft X-ray low state). We found that the source was extremely variable, with many bright flares. The flares have relatively symmetric time profiles. There are a few time intervals where the flux rises steadily and then drops suddenly, sometimes to a level lower than the average before the increase. Hardness ratios showed that the source was slightly softer when the flux was brighter. The power density spectra (PDS) were also complicated and we found that broken power laws do not provide adequate fits to any of them. Instead a pair of zero-centered Lorentzians gives a good general description of the shape of the PDS. We found several quasi-periodic oscillations (QPO), including some that are harmonically spaced with the most stable frequency at 0.35 Hz. While the overall rms variability of the source was close to being constant throughout the observation (29% integrating between 0.01 and 50 Hz), there is a small but significant change in the PDS shape with time. More importantly, we show that the soft 2-5 keV band is more variable than the harder 5-10 and 10-40 keV bands, which is unusual for this source and for other black hole candidates. Cross correlation functions (CCF) between these bands show that the light curve for the 10-40 keV band lags that of the 2-5 keV band by 5 msec.Comment: Submitted to Astrophysical Journal. 20 pages. 8 figure

Studying the X-ray hysteresis in GX 339-4: the disc and iron line over one decade

We report on a comprehensive and consistent investigation into the X-ray emission from GX 339-4. All public observations in the 11 year RXTE archive were analysed. Three different types of model - single powerlaw, broken powerlaw and a disc + powerlaw - were fitted to investigate the evolution of the disc, along with a fixed gaussian component at 6.4 keV to investigate any iron line in the spectrum. We show that the relative variation in flux and X-ray colour between the two best sampled outbursts are very similar. The decay of the disc temperature during the outburst is clearly seen in the soft state. The expected decay is S_Disc \propto T^4; we measure T^4.75\pm0.23. This implies that the inner disc radius is approximately constant in the soft state. We also show a significant anti-correlation between the iron line significant width and the X-ray flux in the soft state while in the hard state the EW is independent of the flux. This results in hysteresis in the relation between X-ray flux and both line flux and EW. To compare the X-ray binary outburst to the behaviour seen in AGN, we construct a Disc Fraction Luminosity Diagram for GX 339-4, the first for an X-ray binary. The shape qualitatively matches that produced for AGN. Linking this with the radio emission from GX 339-4 the change in radio spectrum between the disc and power-law dominated states is clearly visible.Comment: Accepted for publication in MNRAS, 20 pages, 17 figures. For high-res version see http://www.astro.soton.ac.uk/~r.j.dunn/publications.htm