We propose a bootstrap detection for operationally deterministic versus stochastic nonlinear modelling and illustrate the method with both simulated and real data sets.

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least...

This paper is concerned with the use of a cross-validation method based on the kernel estimate of the conditional mean for the subset selection of stochastic regressors within the framework of non-linear stochastic regression. Under the assumption that the observations are strictly stationary...

This grant was to support research into nonlinear dynamics in space and time of highly variable populations. The project started in February 1999 at the University of Kent at Canterbury. Due to the change of employment of both Tong and Yao, the grant was transferred to the London School of...

Often for a non-regular parametric hypothesis, a tractable test statistic involves a nuisance parameter. A common practice is to replace the unknown nuisance parameter by its estimator. The validality of such a replacement can only be justified for an infinite sample in the sense that under...