An {l1,l2,l∞}\{l_1,l_2,l_{\infty}\}-Regularization Approach to High-Dimensional Errors-in-variables Models

Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In particular, the literature considered (1) observation errors in the design uniformly bounded by some $\bar \delta$, and (2) zero mean independent observation errors. Under the first assumption, the rates of convergence of the proposed estimators depend explicitly on $\bar \delta$, while the second assumption has been applied when an estimator for the second moment of the observational error is available. This work proposes and studies two new estimators which, compared to other procedures for regression models with errors in the design, exploit an additional $l_{\infty}$-norm regularization. The first estimator is applicable when both (1) and (2) hold but does not require an estimator for the second moment of the observational error. The second estimator is applicable under (2) and requires an estimator for the second moment of the observation error. Importantly, we impose no assumption on the accuracy of this pilot estimator, in contrast to the previously known procedures. As the recent proposals, we allow the number of covariates to be much larger than the sample size. We establish the rates of convergence of the estimators and compare them with the bounds obtained for related estimators in the literature. These comparisons show interesting insights on the interplay of the assumptions and the achievable rates of convergence

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

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

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

Evidence for reduced magnetic braking in polars from binary population models

We present the first population synthesis of synchronous magnetic cataclysmic variables, called polars, taking into account the effect of the white dwarf (WD) magnetic field on angular momentum loss. We implemented the reduced magnetic braking (MB) model proposed by Li, Wu & Wickramasinghe into the Binary Stellar Evolution (BSE) code recently calibrated for cataclysmic variable (CV) evolution. We then compared separately our predictions for polars and non-magnetic CVs with a large and homogeneous sample of observed CVs from the Sloan Digital Sky Survey. We found that the predicted orbital period distributions and space densities agree with the observations if period bouncers are excluded. For polars, we also find agreement between predicted and observed mass transfer rates, while the mass transfer rates of non-magnetic CVs with periods ≳3 h drastically disagree with those derived from observations. Our results provide strong evidence that the reduced MB model for the evolution of highly magnetized accreting WDs can explain the observed properties of polars. The remaining main issues in our understanding of CV evolution are the origin of the large number of highly magnetic WDs, the large scatter of the observed mass transfer rates for non-magnetic systems with periods ≳3 h, and the absence of period bouncers in observed samples

Origin of the X-ray Quasi-Periodic Oscillations and Identification of a Transient Ultraluminous X-Ray Source in M82

The starburst galaxy M82 contains two ultraluminous X-ray sources (ULXs), CXOM82 J095550.2+694047 (=X41.4+60) and CXOM82 J095551.1+694045 (=X42.3+59), which are unresolved by XMM-Newton. We revisited the two XMM-Newton observations of M82 and analyzed the surface brightness profiles using the known Chandra source positions. We show that the quasi-periodic oscillations (QPOs) detected with XMM-Newton originate from X41.4+60, the brightest X-ray source in M82. Correcting for the contributions of the unresolved sources, the QPO at a frequency of 55.8+/-1.3 mHz on 2001 May 06 had a fractional rms amplitude of 32%, and the QPO at 112.9+/-1.3 mHz on 2004 April 21 had an amplitude of 21%. The QPO frequency may possibly be correlated with the source flux, similar to the type C QPOs in XTE 1550-564 and GRS 1915+105, but at luminosities two orders of magnitude higher. X42.3+59, the second brightest source in M82, displayed a strikingly high flux of 1.4E-11 ergs/cm^2/s in the 2-10 keV band on 2001 May 6. A seven-year light curve of X42.3+59 shows extreme variability over a factor of 1000; the source is not detected in several Chandra observations. This transient behavior suggests accretion from an unstable disk. If the companion star is massive, as might be expected in the young stellar environment, then the compact object would likely be an IMBH.Comment: 9 pages, 6 figures, submitted to ApJ on May 08, 200

Discovery of two simultaneous non-harmonically related Quasi-Periodic Oscillations in the 2005 outburst of the black-hole binary GRO J1655-40

We studied the low-frequency quasi-periodic oscillations (LFQPOs) in the black hole GRO J1655-40 during the 2005 outburst, using data from the Rossi X-ray Timing Explorer. All LFQPOs could be identified as either type B or type C using previously proposed classification schemes. In the soft state of the outburst the type-C LFQPOs reached frequencies that are among the highest ever seen for LFQPOs in black holes. At the peak of the outburst, in the ultra-luminous state, the power spectrum showed two simultaneous, non-harmonically related peaks which we identified as a type-B and a type-C QPO. The simultaneous presence of a type-C and type-B QPO shows that at least two of the three known LFQPO types are intrinsically different and likely the result of distinct physical mechanisms. We also studied the properties of a broad peaked noise component in the power spectra of the ultra-luminous state. This noise component becomes more coherent with count rate and there are strong suggestions that it evolves into a type-B QPO at the highest observed count rates.Comment: 14 pages, 6 figures, 2 tables, accepted for publication in MNRA