NonpModelCheck: An R Package for Nonparametric Lack-of-Fit Testing and Variable Selection

We describe the R package NonpModelCheck for hypothesis testing and variable selection in nonparametric regression. This package implements functions to perform hypothesis testing for the significance of a predictor or a group of predictors in a fully nonparametric heteroscedastic regression model using high-dimensional one-way ANOVA. Based on the p values from the test of each covariate, three different algorithms allow the user to perform variable selection using false discovery rate corrections. A function for classical local polynomial regression is implemented for the multivariate context, where the degree of the polynomial can be as large as needed and bandwidth selection strategies are built in

Linear Regression for Astronomical Data with Measurement Errors and Intrinsic Scatter

Two new methods are proposed for linear regression analysis for data with measurement errors. Both methods are designed to accommodate intrinsic scatter in addition to measurement errors. The first (BCES) is a direct extension of the ordinary least squares (OLS) estimator to allow for measurement errors. It is quite general, allowing a) for measurement errors on both variables, b) the measurement errors for the two variables to be dependent, c) the magnitudes of the measurement errors to depend on the measurements, and d) other `symmetric' lines such as the bisector and the orthogonal regression can be constructed. The second method is a weighted least squares (WLS) estimator, which applies only in the case where the `independent' variable is measured without error and the magnitudes of the measurement errors on the 'dependent' variable are independent from the measurements. Several applications are made to extragalactic astronomy: The BCES method, when applied to data describing the color-luminosity relations for field galaxies, yields significantly different slopes than OLS and other estimators used in the literature. Simulations with artificial data sets are used to evaluate the small sample performance of the estimators. Unsurprisingly, the least-biased results are obtained when color is treated as the dependent variable. The Tully-Fisher relation is another example where the BCES method should be used because errors in luminosity and velocity are correlated due to inclination corrections. We also find, via simulations, that the WLS method is by far the best method for the Tolman surface-brightness test, producing the smallest variance in slope by an order of magnitude. Moreover, with WLS it is not necessary to ``reduce'' galaxies to a fiducial surface-brightness, since this model incorporates intrinsic scatter.Comment: 23 pages LaTeX, 1 postscript table, and style files (uuencoded, gzipp'ed tar file). To appear in the Astrophysical Journal, October 10, 1996 issue, Vol. 47

Testing for Main Random Effects in Two-Way Random and Mixed Effects Models: Modifying the Statistic

A procedure for testing the significance of the main random effect is proposed under a model which does not require the traditional assumptions of symmetry, homoscedasticity, and normality for the error term and random effects. To accommodate this level of model generality, and also unbalanced designs, suitable adjustments to the F-test are made. The extensive simulations performed under the random effects model, and the unrestricted and restricted versions of the mixed effects model, indicate that the classical F procedure is extremely liberal under heteroscedasticity and unbalancedness. The proposed test procedure performs well in all settings and is comparable to the classical F-test when the classical assumptions are met. An analysis of a dataset from the Mussel Watch Project is presented

TWO-WAY HETEROSCEDASTIC ANOVA WHEN THE NUMBER OF LEVELS IS LARGE

Abstract: We consider testing for main treatment effects and interaction effects in crossed two-way layouts when one or both factors have large number of levels. Random errors are allowed to be nonnormal and heteroscedastic. In the heteroscedastic case, we propose new test statistics. The asymptotic distributions of our test statistics are derived under both the null hypothesis and local alternatives. The sample size per treatment combination can either be fixed or tend to infinity. Numerical simulations indicate that the proposed procedures have good power properties and maintain approximately the nominal α-level with small sample sizes. A data set from a study evaluating forty varieties of winter wheat in a large-scale agricultural trial is analyzed

Chandra and XMM-Newton observations of the first quasars: X-rays from the age of cosmic enlightenment

We report on Chandra and XMM-Newton observations of a sample of 13 quasars at z~4.7-5.4 mostly taken from the Sloan Digital Sky Survey (SDSS). The present sample complements previous X-ray studies of z>4 quasars, in which the majority of the objects are optically more luminous and at lower redshifts. All but two of our quasars have been detected in the X-ray band, thus doubling the number of z>4.8 X-ray detected quasars. The two non-detections are likely to be due to a short exposure time and to the presence of intrinsic absorption. We confirm and extend to the highest redshifts the presence of a correlation between AB1450(1+z) magnitude and soft X-ray flux for z>4 quasars, and the presence of a steeper optical-to-X-ray spectral energy distribution (parameterized by aox) for high-luminosity, high-redshift quasars than for lower-luminosity, lower-redshift quasars. The second effect is likely due to the known anti-correlation between aox and rest-frame 2500 Angstrom luminosity, whose significance is confirmed via partial correlation analysis. The joint ~2.5-36 keV rest-frame spectrum of the z>4.8 SDSS quasars observed thus far by Chandra is well parameterized by a power-law with photon index Gamma=1.84+/-0.30; this photon index is consistent with those of z~0-3 quasars and that obtained from joint spectral fitting of z~4.1-4.5 optically luminous Palomar Digital Sky Survey quasars. No evidence for widespread intrinsic X-ray absorption has been found (Nh<4.0x10^{22} cm^{-2} on average at 90% confidence). We also obtained Hobby-Eberly Telescope (HET) photometric observations for eight of our target quasars. None of these shows significant (>30%) optical variability over the time interval of a few years (in the observed frame) between the SDSS and HET observations.Comment: 15 pages (8 figures), LaTeX emulateapj5.sty, accepted for publication by The Astronomical Journal (June 2003

An X-ray Spectral Survey of Radio-Loud AGN With ASCA

We present a uniform and systematic analysis of the 0.6-10 keV X-ray spectra of radio-loud active galactic nuclei (AGN) observed by ASCA. The sample 10 BLRGs, 5 QSRs, 9 NLRGs, and 10 RGs. At soft X-rays, about half of the NLRGs and all of the RGs exhibit a thermal plasma component, with a bimodal distribution of temperatures and luminosities, suggesting an origin either in a surrounding cluster or loose group or in a hot corona. At energies above 2 keV, a hard power-law component is detected in 90% of cases. The power-law photon indices and luminosities in BLRGs, QSRs, and NLRGs are similar, consistent with orientation-based unification schemes. Significant excess cold absorption is detected in most NLRGs, but also in some BLRGS and QSRs, which was somewhat unexpected. In contrast to Seyfert galaxies, only one object showss the signature of a warm absorber. The nuclear X-ray luminosity is correlated with the luminosity of the [O III] emission line, the FIR emission at 12 microns, and the lobe radio power at 5 GHz. The Fe K line is detected in 50% of BLRGs, one QSR, and a handful of NLRGs. This sample also includes 6 Weak Line Radio Galaxies (WLRGs). Their spectra WLRGs can be generally decomposed into a soft thermal component with hard absrorbed power-law component, which is significantly flatter than any other radio-loud AGNs. Their intrinsic luminosities are two orders of magnitude lower than in other sources of the sample. An interesting possibility is that WLRGs represent an extreme population of radio galaxies in which the central black hole is accreting at a rate well below the Eddington rate.Comment: To appear in the Astrophysical Journal. 72 pages, including many tables and figures. Fig 1 is separate, in TIFF format. Postscript version of fig 1 and postscript version of entire preprint can be obtained from http://www.astro.psu.edu/users/mce/preprint_index.htm

A note on contiguity and L1-norm

The interrelationship between the property of contiguity of two sequences of probability measures {Pn} and {Qn} and the convergence to zero of [short parallel]Pn - Qn[short parallel] is extendended and clarified.Contiguity L1-norm