Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

Consistency of the mass variation formula for black holes accreting cosmological fluids

We address the spherical accretion of generic fluids onto black holes. We show that, if the black hole metric satisfies certain conditions, in the presence of a test fluid it is possible to derive a fully relativistic prescription for the black hole mass variation. Although the resulting equation may seem obvious due to a form of it appearing as a step in the derivation of the Schwarzschild metric, this geometrical argument is necessary to fix the added degree of freedom one gets for allowing the mass to vary with time. This result has applications on cosmological accretion models and provides a derivation from first principles to serve as a basis to the accretion equations already in use in the literature.

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Dahlberg formula: a novel approach for its evaluation

INTRODUCTION: The accurate evaluation of error of measurement (EM) is extremely important as in growth studies as in clinical research, since there are usually quantitatively small changes. In any study it is important to evaluate the EM to validate the results and, consequently, the conclusions. Because of its extreme simplicity, the Dahlberg formula is largely used worldwide, mainly in cephalometric studies. OBJECTIVES: (I) To elucidate the formula proposed by Dahlberg in 1940, evaluating it by comparison with linear regression analysis; (II) To propose a simple methodology to analyze the results, which provides statistical elements to assist researchers in obtaining a consistent evaluation of the EM. METHODS: We applied linear regression analysis, hypothesis tests on its parameters and a formula involving the standard deviation of error of measurement and the measured values. RESULTS AND CONCLUSION: we introduced an error coefficient, which is a proportion related to the scale of observed values. This provides new parameters to facilitate the evaluation of the impact of random errors in the research final results.

Lê–Greuel type formula for the Euler obstruction and applications

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel type formulas for germs f:(X,0)→(C,0) and g:(X,0)→(C,0). We give applications when g is a generic linear form and when f and g have isolated singularities.