A1104
Title: Ratio tests using the Cauchy distribution: A simple principle
Authors: Uwe Hassler - Goethe University Frankfurt (Germany) [presenting]
Mehdi Hosseinkouchack - Goethe University Frankfurt (Germany)
Abstract: A testing principle is introduced by building on two weighted partial sample sums. Under general assumptions, both sums are asymptotically normal. Upon normalization and orthogonalization, the ratio thus converges to the standard Cauchy distribution. Critical values and p-values are hence readily available, and local power can be computed against specific alternative hypotheses. At the same time, a potential nuisance scaling parameter cancels from the ratio making these Cauchy tests self-normalizing. wo examples are discussed: a test for the null of zero mean random variables and a test for the null of a unit root in time series. Both examples result in a limiting Wiener process. Asymptotic local power is evaluated against different alternatives. The weights in the numerator and denominator are from the Karhunen-Loeve expansion of the Wiener process. The power crucially hinges on the specific weighting schemes used to compute the test statistics. Finally, this Cauchy test principle is carried to a multivariate framework of several correlated samples. Here, the cross-covariances between the samples reduce to one scaling parameter that cancels from the Cauchy ratios due to self-normalization. The tests are robust with respect to cross-dependence without the need to estimate nuisance parameters.
