We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed...

Motivated by interval/region prediction in nonlinear time series, we propose a minimum volume predictor (MV-predictor) for a strictly stationary process. The MV-predictor varies with respect to the current position in the state space and has the minimum Lebesgue measure among all regions with...

We consider a conditional empirical distribution of the form Fn(C ∣ x)=∑nt=1 ωn(Xt−x) I{Yt∈C} indexed by C∈ ℓ, where {(Xt, Yt), t=1, …, n} are observations from a strictly stationary and strong mixing stochastic process, {ωn(Xt−x)} are kernel weights, and ℓ is a class of...

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...

For spatio-temporal regression models with observations taken regularly in time but irregularly over space, we investigate the effect of spatial smoothing on the reduction of variance in estimating both parametric and nonparametric regression functions. The processes concerned are stationary in...

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...

We propose a new method to determine the cointegration rank in the error correction model of Engle and Granger (1987). To this end, we first estimate the cointegration vectors in terms of a residual-based principal component analysis. Then the cointegration rank, together with the lag order, is...