Inference in Linear Regression Models with Many Covariates and Heteroskedasticity

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates are allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker-White heteroskedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional)\ heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is also provided. The proposed methods are also illustrated with an empirical application

Final Report: Wall Effects in Cavity Flows

The wall effects in cavity flows past an arbitrary two-dimensional body is investigated for both pure-drag and lifting cases based on an inviscid nonlinear flow theory. The over-all features of various theoretical flow models for inviscid cavity flows under the wall effects are discussed from the general momentum consideration in comparison with typical viscous, incompressible wake flows in a channel. In the case of pure drag cavity flows, three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant jet models, are applied to evaluate the solution. Methods of numerical computation are discussed for bodies of arbitrary shape, and are carried out in detail for wedges of all angles. The final numerical results are compared between the different flow models, and the differences pointed out. Further analysis of the results has led to development of several useful formulas for correcting the wall effect. In the lifting flow case, the wall effect on the pressure and hydrodynamic forces acting on arbitrary body is formulated for the choked cavity flow in a closed water tunnel of arbitrary shape, and computed for the flat plate with a finite cavity in a straight tunnel

A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix

This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.

Determining the Contribution of Epidermal Cell Shape to Petal Wettability Using Isogenic Antirrhinum Lines

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

The youngest massive protostars in the Large Magellanic Cloud

We demonstrate the unique capabilities of Herschel to study very young luminous extragalactic young stellar objects (YSOs) by analyzing a central strip of the Large Magellanic Cloud obtained through the HERITAGE Science Demonstration Program. We combine PACS 100 and 160, and SPIRE 250, 350, and 500 microns photometry with 2MASS (1.25-2.17 microns) and Spitzer IRAC and MIPS (3.6-70 microns) to construct complete spectral energy distributions (SEDs) of compact sources. From these, we identify 207 candidate embedded YSOs in the observed region, ~40% never-before identified. We discuss their position in far-infrared color-magnitude space, comparing with previously studied, spectroscopically confirmed YSOs and maser emission. All have red colors indicating massive cool envelopes and great youth. We analyze four example YSOs, determining their physical properties by fitting their SEDs with radiative transfer models. Fitting full SEDs including the Herschel data requires us to increase the size and mass of envelopes included in the models. This implies higher accretion rates (greater than or equal to 0.0001 M_sun/yr), in agreement with previous outflow studies of high-mass protostars. Our results show that Herschel provides reliable longwave SEDs of large samples of high-mass YSOs; discovers the youngest YSOs whose SEDs peak in Herschel bands; and constrains the physical properties and evolutionary stages of YSOs more precisely than was previously possible.Comment: Main text: 4 pages, 3 figures, 1 table; Online material: 3 figures, 1 table; to appear in the A&A Herschel Special Issu

Nowhere minimal CR submanifolds and Levi-flat hypersurfaces

A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces.Comment: 21 pages; conjecture 2.8 was removed in proof; to appear in J. Geom. Ana

Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.Comment: Latex (Revtex) source + 13 small postscript figures. Revised versio

Can Reflection from Grains Diagnose the Albedo?

By radiation transfer models with a realistic power spectra of the projected density distributions, we show that the optical properties of grains are poorly constrained by observations of reflection nebulae. The ISM is known to be hierarchically clumped from a variety of observations (molecules, H I, far-infrared). Our models assume the albedo and phase parameter of the dust, the radial optical depth of the sphere averaged over all directions, and random distributions of the dust within the sphere. The outputs are the stellar extinction, optical depth, and flux of scattered light as seen from various viewing angles. Observations provide the extinction and scattered flux from a particular direction. Hierarchical geometry has a large effect on the flux of scattered light emerging from a nebula for a particular extinction of the exciting star. There is a very large spread in both scattered fluxes and extinctions for any distribution of dust. Consequently, an observed stellar extinction and scattered flux can be fitted by a wide range of albedos. With hierarchical geometry it is not completely safe to determine even relative optical constants from multiwavelength observations of the same reflection nebula. The geometry effectively changes with wavelength as the opacity of the clumps varies. Limits on the implications of observing the same object in various wavelengths are discussed briefly. Henry (2002) uses a recipe to determine the scattered flux from a star with a given extinction. It is claimed to be independent of the geometry. It provides considerably more scattering than our models, probably leading to an underestimate of the grain albedos from the UV Diffuse Galactic Light.Comment: 27 pages, including 7 figures. Accepted by Ap

Star Formation and Young Population of the HII Complex Sh2-294

The Sh2-294 HII region ionized by a single B0V star features several infrared excess sources, a photodissociation region, and also a group of reddened stars at its border. The star formation scenario in the region seems to be quite complex. In this paper, we present follow-up results of Sh2-294 HII region at 3.6, 4.5, 5.8, and 8.0 microns observed with the Spitzer Space Telescope Infrared Array Camera (IRAC), coupled with H2 (2.12 microns) observation, to characterize the young population of the region and to understand its star formation history. We identified 36 young stellar object (YSO, Class I, Class II and Class I/II) candidates using IRAC color-color diagrams. It is found that Class I sources are preferentially located at the outskirts of the HII region and associated with enhanced H2 emission; none of them are located near the central cluster. Combining the optical to mid-infrared (MIR) photometry of the YSO candidates and using the spectral energy distribution fitting models, we constrained stellar parameters and the evolutionary status of 33 YSO candidates. Most of them are interpreted by the model as low-mass (< 4 solar masses) YSOs; however, we also detected a massive YSO (~9 solar masses) of Class I nature, embedded in a cloud of visual extinction of ~24 mag. Present analysis suggests that the Class I sources are indeed younger population of the region relative to Class II sources (age ~ 4.5 x 10^6 yr). We suggest that the majority of the Class I sources, including the massive YSOs, are second-generation stars of the region whose formation is possibly induced by the expansion of the HII region powered by a ~ 4 x 10^6 yr B0 main-sequence star.Comment: 12 pages, 7 figures, 2 tables. Accepted for publication in The Astrophysical Journa