Statistics Seminar: Qiying Wang -- Martingale limit theorems revisited and non-linear cointegrating regression

Qiying Wang School of Mathematics and Statistics University of Sydney 

Location: Carslaw 173 

Time: 2pm Friday, March 25, 2011 

Title: Martingale limit theorems revisited and non-linear cointegrating regression 

Abstract: For a certain class of martingales, the convergence to mixture normal
distribution is established under the convergence in distribution for the conditional
variance.  This is less restrictive in comparison with the classical martingale limit
theorem where one generally requires the convergence in probability.  The extension
removes a main barrier in the applications of the classical martingale limit theorem to
non-parametric estimates and inferences with non-stationarity, and essentially enhances
the effectiveness of the classical martingale limit theorem as one of the main tools in
the investigation of asymptotics in statistics, econometrics and other fields.  The main
result is applied to the investigations of asymptotics for the conventional kernel
estimator in a nonlinear cointegrating regression, which essentially improves the
existing works in literature.