A Monte Carlo Investigation of Some Tests for Stochastic Dominance

This paper compares the performance of several tests for stochastic dominance up to order three using Monte Carlo methods. The tests considered are the Davidson and Duclos (2000) test, the Anderson test (1996) and the Kaur, Rao and Singh (1994) test. Only unpaired samples of independent observations are considered, as this is a restriction for both the Anderson and Kaur-Rao-Singh tests. We find that the Davidson-Duclos test appears to be the best. The Kaur-Rao-Singh test is overly conservative and does not compare favorably against the Davidson-Duclos and Anderson tests in terms of power.Burr distribution, Income distribution, Monte Carlo method, Portfolio investment, Stochastic dominance, Union-intersection test

A Comparison of highly efficient iterative linear solvers

A number of iterative techniques have recently been developed which are extremely efficient at solving systems of linear equations. Of these methods probably the most recognized is the Conjugate Gradient Method (CG). This is an extremely efficient solver and has been used successfully for a number of years now. A newer method proposed initially by Davidson [1] is studied in this paper. This method has proven itself in terms of efficiency by solving the same system (of order 2000) that was solved by the CG method. It converged in approximately 40 iterations, taking less than five minutes to do so[5], compared to the CG method which took nearly 100 iterations, converging after about 1 5 minutes. Very little documentation about the derivation or development of Davidson\u27s method exists, and his paper was written in terms of an eigenvalue problem. A portion of a program developed by NASA Ames Research Center uses a variation of Davidson\u27s method as a linear solver. Davidson\u27s method was explored and derived using his paper and the FORTRAN code from NASA. The purpose of this thesis is to provide some insight into the analytical aspect of Davidson\u27s method, using the CG method for comparison

Restarting parallel Jacobi-Davidson with both standard and harmonic Ritz values

We study the Jacobi-Davidson method for the solution of large generalized eigenproblems as they arise in MagnetoHydroDynamics. We have combined Jacobi-Davidson (using standard Ritz values) with a shift and invert technique. We apply a complete LU decomposition in which reordering strategies based on a combination of block cyclic reduction and domain decomposition result in a well-parallelizable algorithm. Moreover, we describe a variant of Jacobi-Davidson in which harmonic Ritz values are used. In this variant the same parallel LU decomposition is used, but this time as a preconditioner to solve the `correction` equation. The size of the relatively small projected eigenproblems which have to be solved in the Jacobi-Davidson method is controlled by several parameters. The influence of these parameters on both the parallel performance and convergence behaviour will be studied. Numerical results of Jacobi-Davidson obtained with standard and harmonic Ritz values will be shown. Executions have been performed on a Cray T3E