This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test...

This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for testing whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed...

This paper establishes a general moment inequality for spatial processes satisfying the [alpha]-mixing condition [cf., Tran, 1990. Kernel density estimation on random fields. J. Multivariate Analy. 34, 37-53]. Such a general moment inequality is a nontrivial extension of the corresponding result...

We propose to approximate the conditional expectation of a spatial random variable given its nearest-neighbour observations by an additive function. The setting is meaningful in practice and requires no unilateral ordering. It is capable of catching nonlinear features in spatial data and...

We have established the asymptotic theory for the estimation of adaptive varying-coe�cient linear models. More speci�cally we have shown that the estimator for the global index parameter is root-n consistent without imposing, as a prerequisite, that the estimator is within n

We propose an adaptive varying-coefficient spatiotemporal model for data that are observed irregularly over space and regularly in time. The model is capable of catching possible non-linearity (both in space and in time) and non-stationarity (in space) by allowing the auto-regressive...

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...

Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given...

Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given...

Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given...