Orthogonal Methods for Generating Large Positive Semi-Definite Covariance Matrices

It is a common problem in risk management today that risk measures and pricing models are being applied to a very large set of scenarios based on movements in all possible risk factors. The dimensions are so large that the computations become extremely slow and cumbersome, so it is quite common that over-simplistic assumptions will be made. In particular, in order to generate the large covariance matrices that are used in Value-at-Risk models, some very strong constraints are imposed on the movements in volatility and correlations in all the standard models. The constant volatility assumption is also imposed, because it has not been possible to generate large GARCH covariance matrices with mean-reverting term structures.

Calibrated Weighting for Small Area Estimation

Calibrated weighting methods for estimation of survey population characteristics are widely used. At the same time, model-based prediction methods for estimation of small area or domain characteristics are becoming increasingly popular. This paper explores weighting methods based on the mixed models that underpin small area estimates to see whether they can deliver equivalent small area estimation performance when compared with standard prediction methods and superior population level estimation performance when compared with standard calibrated weighting methods. A simple MSE estimator for weighted small area estimation is also developed

Consistency of cosmic microwave background temperature measurements in three frequency bands in the 2500-square-degree SPT-SZ survey

We present an internal consistency test of South Pole Telescope (SPT) measurements of the cosmic microwave background (CMB) temperature anisotropy using three-band data from the SPT-SZ survey. These measurements are made from observations of ~2500 deg^2 of sky in three frequency bands centered at 95, 150, and 220 GHz. We combine the information from these three bands into six semi-independent estimates of the CMB power spectrum (three single-frequency power spectra and three cross-frequency spectra) over the multipole range 650 < l < 3000. We subtract an estimate of foreground power from each power spectrum and evaluate the consistency among the resulting CMB-only spectra. We determine that the six foreground-cleaned power spectra are consistent with the null hypothesis, in which the six cleaned spectra contain only CMB power and noise. A fit of the data to this model results in a chi-squared value of 236.3 for 235 degrees of freedom, and the probability to exceed this chi-squared value is 46%.Comment: 21 pages, 4 figures, current version matches version published in JCA

Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results

(Abridged) New full sky temperature and polarization maps based on seven years of data from WMAP are presented. The new results are consistent with previous results, but have improved due to reduced noise from the additional integration time, improved knowledge of the instrument performance, and improved data analysis procedures. The improvements are described in detail. The seven year data set is well fit by a minimal six-parameter flat Lambda-CDM model. The parameters for this model, using the WMAP data in conjunction with baryon acoustic oscillation data from the Sloan Digital Sky Survey and priors on H_0 from Hubble Space Telescope observations, are: Omega_bh^2 = 0.02260 +-0.00053, Omega_ch^2 = 0.1123 +-0.0035, Omega_Lambda = 0.728 +0.015 -0.016, n_s = 0.963 +-0.012, tau = 0.087 +-0.014 and sigma_8 = 0.809 +-0.024 (68 % CL uncertainties). The temperature power spectrum signal-to-noise ratio per multipole is greater that unity for multipoles < 919, allowing a robust measurement of the third acoustic peak. This measurement results in improved constraints on the matter density, Omega_mh^2 = 0.1334 +0.0056 -0.0055, and the epoch of matter- radiation equality, z_eq = 3196 +134 -133, using WMAP data alone. The new WMAP data, when combined with smaller angular scale microwave background anisotropy data, results in a 3 sigma detection of the abundance of primordial Helium, Y_He = 0.326 +-0.075.The power-law index of the primordial power spectrum is now determined to be n_s = 0.963 +-0.012, excluding the Harrison-Zel'dovich-Peebles spectrum by >3 sigma. These new WMAP measurements provide important tests of Big Bang cosmology.Comment: 42 pages, 9 figures, Submitted to Astrophysical Journal Supplement Serie

Optimized differential energy loss estimation for tracker detectors

The estimation of differential energy loss for charged particles in tracker detectors is studied. The robust truncated mean method can be generalized to the linear combination of the energy deposit measurements. The optimized weights in case of arithmetic and geometric means are obtained using a detailed simulation. The results show better particle separation power for both semiconductor and gaseous detectors.Comment: 16 pages, 8 figures, submitted to Nucl. Istrum. Meth.

Measurements of Sub-degree B-mode Polarization in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data

We present a measurement of the $B$-mode polarization power spectrum (the $BB$ spectrum) from 100 $\mathrm{deg}^2$ of sky observed with SPTpol, a polarization-sensitive receiver currently installed on the South Pole Telescope. The observations used in this work were taken during 2012 and early 2013 and include data in spectral bands centered at 95 and 150 GHz. We report the $BB$ spectrum in five bins in multipole space, spanning the range $300 \le \ell \le 2300$, and for three spectral combinations: 95 GHz $\times$ 95 GHz, 95 GHz $\times$ 150 GHz, and 150 GHz $\times$ 150 GHz. We subtract small ($< 0.5 \sigma$ in units of statistical uncertainty) biases from these spectra and account for the uncertainty in those biases. The resulting power spectra are inconsistent with zero power but consistent with predictions for the $BB$ spectrum arising from the gravitational lensing of $E$-mode polarization. If we assume no other source of $BB$ power besides lensed $B$ modes, we determine a preference for lensed $B$ modes of $4.9 \sigma$. After marginalizing over tensor power and foregrounds, namely polarized emission from galactic dust and extragalactic sources, this significance is $4.3 \sigma$. Fitting for a single parameter, $A_\mathrm{lens}$, that multiplies the predicted lensed $B$-mode spectrum, and marginalizing over tensor power and foregrounds, we find $A_\mathrm{lens} = 1.08 \pm 0.26$, indicating that our measured spectra are consistent with the signal expected from gravitational lensing. The data presented here provide the best measurement to date of the $B$-mode power spectrum on these angular scales.Comment: 21 pages, 4 figure