Multivariate Location: Robust Estimators And Inference

The sample mean can have poor efficiency relative to various alternative estimators under arbitrarily small departures from normality. In the multivariate case, (affine equivariant) estimators have been proposed for dealing with this problem, but a comparison of various estimators by Massé and Plante (2003) indicated that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the skipped estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal distributions

Within Groups Multiple Comparisons Based On Robust Measures Of Location

Consider the problem of performing all pair-wise comparisons among J dependent groups based on measures of location associated with the marginal distributions. It is well known that the standard error of the sample mean can be large relative to other estimators when outliers are common. Two general strategies for addressing this problem are to trim a fixed proportion of observations or empirically check for outliers and remove (or down-weight) any that are found. However, simply applying conventional methods for means to the data that remain results in using the wrong standard error. Methods that address this problem have been proposed, but among the situations considered in published studies, no method has been found that gives good control over the probability of a Type I error when sample sizes are small (less than or equal to thirty); the actual probability of a Type I error can drop well below the nominal level. The paper suggests using a slight generalization of a percentile bootstrap method to address this problem

Study of fuel cell on-site, integrated energy systems in residential/commercial applications

Three building applications were selected for a detailed study: a low rise apartment building; a retail store, and a hospital. Building design data were then specified for each application, based on the design and construction of typical, actual buildings. Finally, a computerized building loads analysis program was used to estimate hourly end use load profiles for each building. Conventional and fuel cell based energy systems were designed and simulated for each building in each location. Based on the results of a computer simulation of each energy system, levelized annual costs and annual energy consumptions were calculated for all systems

A Study of Giant Pulses from PSR J1824-2452A

We have searched for microsecond bursts of emission from millisecond pulsars in the globular cluster M28 using the Parkes radio telescope. We detected a total of 27 giant pulses from the known emitter PSR J1824-2452A. At wavelengths around 20 cm the giant pulses are scatter-broadened to widths of around 2 microseconds and follow power-law statistics. The pulses occur in two narrow phase-windows which correlate in phase with X-ray emission and trail the peaks of the integrated radio pulse-components. Notably, the integrated radio emission at these phase windows has a steeper spectral index than other emission. The giant pulses exhibit a high degree of polarization, with many being 100% elliptically polarized. Their position angles appear random. Although the integrated emission of PSR J1824-2452A is relatively stable for the frequencies and bandwidths observed, the intensities of individual giant pulses vary considerably across our bands. Two pulses were detected at both 2700 and 3500 MHz. The narrower of the two pulses is 20 ns wide at 3500 MHz. At 2700 MHz this pulse has an inferred brightness temperature at maximum of 5 x 10^37 K. Our observations suggest the giant pulses of PSR J1824-2452A are generated in the same part of the magnetosphere as X-ray emission through a different emission process to that of ordinary pulses.Comment: Accepted by Ap

Preliminary Testing for Normality: Is This a Good Practice?

Normality is a distributional requirement of classical test statistics. In order for the test statistic to provide valid results leading to sound and reliable conclusions this requirement must be satisfied. In the not too distant past, it was claimed that violations of normality would not likely jeopardize scientific findings (See Hsu & Feldt, 1969; Lunney, 1970). Recent revelations suggest otherwise (See e.g., Micceri, 1989; Keselman, Huberty, Lix et al., 1998; Erceg-Hurn, Wilcox, & Keselman, 2013; Wilcox and Keselman, 2003; Wilcox, 2012a, b). Unfortunately the data obtained in psychological investigations rarely, if ever, meet the requirement of normally distributed data (Micceri, 1989; Wilcox, 2012a, b). Consequently, it could be the case that the results from many of the investigations conducted in psychology provide invalid results. Accordingly, authors recommend that researchers attempt to assess the validity of assuming data are normal in form prior to conducting a test of significance (Erceg-Hurn, et al., 2013; Keselman, et al., 1998). Present evidence suggests that a popular fit-statistic, the Kolmogorov-Smirnov test does a poor job of evaluating whether data are normal. Our investigation based on this statistic and other fit-statistics provides a more favorable picture of preliminary testing for normality

Trimming, Transforming Statistics, And Bootstrapping: Circumventing the Biasing Effects Of Heterescedasticity And Nonnormality

Researchers can adopt different measures of central tendency and test statistics to examine the effect of a treatment variable across groups (e.g., means, trimmed means, M-estimators, & medians. Recently developed statistics are compared with respect to their ability to control Type I errors when data were nonnormal, heterogeneous, and the design was unbalanced: (1) a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically, (2) two different transformations to eliminate skewness, (3) the accuracy of assessing statistical significance with a bootstrap methodology was examined, and (4) statistics that use a robust measure of the typical score that empirically determined whether data should be trimmed, and, if so, in which direction, and by what amount were examined. The 56 procedures considered were remarkably robust to extreme forms of heterogeneity and nonnormality. However, we recommend a number of Welch-James heteroscedastic statistics which are preceded by the Babu, Padmanaban, and Puri (1999) test for symmetry that either symmetrically trimmed 10% of the data per group, or asymmetrically trimmed 20% of the data per group, after which either Johnson\u27s (1978) or Hall\u27s (1992) transformation was applied to the statistic and where significance was assessed through bootstrapping. Close competitors to the best methods were found that did not involve a transformation

Geometric scaling in high-energy QCD at nonzero momentum transfer

We show how one can obtain geometric scaling properties from the Balitsky-Kovchegov (BK) equation. We start by explaining how, this property arises for the b-independent BK equation. We show that it is possible to extend this model to the full BK equation including momentum transfer. The saturation scale behaves like max(q,Q_T) where q is the momentum transfer and Q_T a typical scale of the target.Comment: 4 pages, 2 figures. Talk given by G. Soyez at the "Rencontres de Moriond", 12-19 March 2005, La Thuile, Ital

Breakdown of Conformal Invariance at Strongly Random Critical Points

We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a strongly random critical point. The average correlation functions of this system demonstrate a breakdown of conformal invariance, while the typical correlation functions demonstrate a breakdown of scale invariance. The breakdown of conformal invariance is due to the vanishing of the correlation functions at the infinite disorder fixed point, causing the critical correlation functions to be controlled by a dangerously irrelevant operator describing the approach to the fixed point. We relate the computation of average correlation functions to a problem of persistence in the RG flow.Comment: 9 page

Imaging Fabry-Perot Spectroscopy of NGC 5775: Kinematics of the Diffuse Ionized Gas Halo

We present imaging Fabry-Perot observations of Halpha emission in the nearly edge-on spiral galaxy NGC 5775. We have derived a rotation curve and a radial density profile along the major axis by examining position-velocity (PV) diagrams from the Fabry-Perot data cube as well as a CO 2-1 data cube from the literature. PV diagrams constructed parallel to the major axis are used to examine changes in azimuthal velocity as a function of height above the midplane. The results of this analysis reveal the presence of a vertical gradient in azimuthal velocity. The magnitude of this gradient is approximately 1 km/s/arcsec, or about 8 km/s/kpc, though a higher value of the gradient may be appropriate in localized regions of the halo. The evidence for an azimuthal velocity gradient is much stronger for the approaching half of the galaxy, although earlier slit spectra are consistent with a gradient on both sides. There is evidence for an outward radial redistribution of gas in the halo. The form of the rotation curve may also change with height, but this is not certain. We compare these results with those of an entirely ballistic model of a disk-halo flow. The model predicts a vertical gradient in azimuthal velocity which is shallower than the observed gradient, indicating that an additional mechanism is required to further slow the rotation speeds in the halo.Comment: 18 pages, 18 figures. Uses emulateapj.cls. Accepted for publication in Ap