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 X-ray Properties of Low-Frequency Quasi-Periodic Oscillations from GRS 1915+105 up to 120 keV

We present a study of the properties of strong 0.8-3.0 Hz quasi-periodic oscillations (QPOs) that occurred during 1997 RXTE observations of the microquasar GRS 1915+105 in the low-hard state. The high count rates allow us to track individual QPO peaks, and we exploit this to develop a QPO folding technique. In contrast to previous QPO studies with RXTE, we emphasize the high energy QPO properties and report the detection of a QPO in the 60-124 keV energy band. Our technique allows us, for the first time, to measure the phase of the QPO harmonics relative to the fundamental. Variation in this phase difference leads to changes in the shape of the QPO profile with energy and over time. The strength of the QPO fundamental increases up to 19 keV, but the data do not suggest that the strength continues to increase above this energy. In some cases, the QPO amplitudes in the 30-60 keV and 60-124 keV energy bands are significantly less than in the 13-19 keV and 19-29 keV energy bands. We also use our technique to measure the phase lag of the QPO fundamental and harmonics. In the case where negative phase lags are detected for the fundamental, positive phase lags are detected for the first harmonic.Comment: Submitted to ApJ, Refereed, 9 page

Least Squares After Model Selection in High-dimensional Sparse Models

http://arxiv.org/abs/1001.0188We study post-model selection estimators which apply ordinary least squares (ols) to the model selected by first-step penalized estimators. It is well known that lasso can estimate the nonparametric regression function at nearly the oracle rate, and is thus hard to improve upon. We show that ols post lasso estimator performs at least as well as lasso in terms of the rate of convergence, and has the advantage of a smaller bias. Remarkably, this performance occurs even if the lasso-based model selection "fails" in the sense of missing some components of the "true" regression model. By the "true" model we mean here the best $s$-dimensional approximation to the nonparametric regression function chosen by the oracle. Furthermore, ols post lasso estimator can perform strictly better than lasso, i.e. a strictly faster rate of convergence, if the lasso-based model selection correctly includes all components of the "true" model as a subset and also achieves sufficient sparsity. In the extreme case, when lasso perfectly selects the "true" model, the ols post lasso estimator becomes the oracle estimator. An important ingredient in our analysis is a new sparsity bound on the dimension of the model selected by lasso which guarantees that this dimension is at most of the same order as the dimension of the "true" model. Moreover, our analysis is not limited to the lasso estimator acting as selector in the first step, but also applies to any other estimator, for example various forms of thresholded lasso, with good rates and good sparsity properties. Our analysis covers both traditional thresholding and a new practical, data-driven thresholding scheme that induces maximal sparsity subject to maintaining a certain goodness-of-fit. The latter scheme has theoretical guarantees similar to those of lasso or ols post lasso, but it dominates these procedures in a wide variety of experiments.National Science Foundation (U.S.

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

High-Dimensional Methods and Inference on Structural and Treatment Effects

Data with a large number of variables relative to the sample size—"high-dimensional data"—are readily available and increasingly common in empirical economics. High-dimensional data arise through a combination of two phenomena. First, the data may be inherently high dimensional in that many different characteristics per observation are available. For example, the US Census collects information on hundreds of individual characteristics and scanner datasets record transaction-level data for households across a wide range of products. Second, even when the number of available variables is relatively small, researchers rarely know the exact functional form with which the small number of variables enter the model of interest. Researchers are thus faced with a large set of potential variables formed by different ways of interacting and transforming the underlying variables. This paper provides an overview of how innovations in "data mining" can be adapted and modified to provide high-quality inference about model parameters. Note that we use the term "data mining" in a modern sense which denotes a principled search for "true" predictive power that guards against false discovery and overfitting, does not erroneously equate in-sample fit to out-of-sample predictive ability, and accurately accounts for using the same data to examine many different hypotheses or models

Iron Line Diagnostics for the GRS 1915+105 Black Hole

The properties of the broad Fe line detected in two BeppoSAX observations of the microquasar GRS 1915+105 are summarized.Comment: 4 pages, 2 figures. Proc. of the II BeppoSAX Meeting: "The Restless High-Energy Universe" (Amsterdam, May 5-8, 2003), E.P.J. van den Heuvel, J.J.M. in 't Zand, and R.A.M.J. Wijers Ed

Quantum mechanical sum rules for two model systems

Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems, the infinite well and the single delta-function potential. These cases illustrate the different ways in which such sum rules can be realized, and the varying mathematical techniques by which they can be confirmed. Using the same methods, we also evaluate the second-order energy shifts arising from the introduction of a constant external field, namely the Stark effect.Comment: 23 pages, no figures, to appear in Am. J. Phy

Burst mode versus single-pulse machining for Bessel beam micro-drilling of thin glass: study and comparison

We present a study on the micro-drilling process by means of a picosecond Bessel-Gauss beam, and the achievements obtained on a 200-mu m-thick AF32 glass sample in different laser fabrication regimes. In particular, we compare the results and morphology of the holes generated with a high-repetition-rate pulsed laser, respectively, in the single-pulse mode and in the burst mode machining regimes. We highlight the advantages or drawbacks of these two types of microfabrication for the generation of through-holes. For a given pulse density, the burst mode turns out to be advantageous with respect to the single-pulse mode fabrication in terms of lower energy per pulse needed and higher speed of drilling, even if the stronger thermal effects can more easily lead to surface cracks. On the other hand, by adjusting the pulse density below a critical level, it can be shown that the single-pulse regime can be adopted for the generation of more regular through-holes and cleaner apertures, even if multiple pass operation is likely to be needed

Photon Propagation Around Compact Objects and the Inferred Properties of Thermally Emitting Neutron Stars

Anomalous X-ray pulsars, compact non-pulsing X-ray sources in supernova remnants, and X-ray bursters are three distinct types of sources for which there are viable models that attribute their X-ray emission to thermal emission from the surface of a neutron star. Inferring the surface area of the emitting regions in such systems is crucial in assessing the viability of different models and in providing bounds on the radii of neutron stars. We show that the inferred areas of the emitting regions may be over- or under-estimated by a factor of <=2, because of the geometry of the system and general relativistic light deflection, combined with the effects of phase averaging. Such effects make the determination of neutron-star radii uncertain, especially when compared to the ~5% level required for constraining the equation of state of neutron-star matter. We also note that, for a given spectral shape, the inferred source luminosities and pulse fractions are anticorrelated because they depend on the same properties of the emitting regions, namely their sizes and orientations, i.e., brighter sources have on average weaker pulsation amplitudes than fainter sources. We argue that this property can be used as a diagnostic tool in distinguishing between different spectral models. As an example, we show that the high inferred pulse fraction and brightness of the pulsar RXS J1708-40 are inconsistent with isotropic thermal emission from a neutron-star surface. Finally, we discuss the implication of our results for surveys in the soft X-rays for young, cooling neutron stars in supernova remnants and show that the absence of detectable pulsations from the compact source at the center of Cas A (at a level of >=30%) is not a strong argument againts its identification with a spinning neutron star.Comment: 6 pages, 6 figures, to appear in the Astrophysical Journal; minor change

Kinematics of Black Hole X-ray Binary GRS 1915+105

The space velocity of a stellar black hole encodes the history of its formation and evolution. Here we measure the 3-dimensional motion of the microquasar GRS 1915+105, using a decade of astrometry with the NRAO Very Long Baseline Array, together with the published radial velocity. The velocity in the Galactic Plane deviates from circular rotation by 53-80 +_ 8 km/s, where the range covers any specific distance from 6-12 kpc. Perpendicular to the plane, the velocity is only 10 +_ 4 km/s. The peculiar velocity is minimized at a distance 9-10 kpc, and is then nearly in the radial direction towards the Galactic Center. We discuss mechanisms for the origin of the peculiar velocity, and conclude that it is most likely a consequence of Galactic velocity diffusion on this old binary, rather than the result of a supernova kick during the formation of the 14 Mo black hole. Finally, a brief comparison is made with 4 other BH binaries whose kinematics are well determined.Comment: 16 pages, 4 figures. ApJ accepte