A rank test for bivariate location and scale problem for elliptically symmetric populations ∗

A nonparametric rank test for the two-sample location and scale bivariate problem is proposed. The asymptotic distribution of the statistic of the test is derived under the null hypothesis and under a class of contiguous alternatives. The asymptotic relative efficiency is given and a simulation study gives the performance of the test and some competitors.     

The Double Gaussian Approximation for High Frequency Data

Abstract High frequency data have become an important feature of many areas of research. They permit the creation of estimators in highly non‐parametric classes of continuous‐time models. In the context of continuous semi‐martingale models, we here provide a locally parametric ‘double Gaussian’ approximation, to facilitate the analysis of estimators. As in Mykland and Zhang (Econometrica, 77, 2009, p. 1403), the error in the approximation can be offset with a postasymptotic likelihood correction. The current approximation is valid in large neighbourhoods, permitting a sharp analysis of estimators that use local behaviour over asymptotically increasing numbers of observations.