In this paper, we study three different types of estimates for the noise-to signal ratios in a general stochastic regression setup. The locally linear and locally quadratic regression estimators serve as the building blocks in our approach. Under the assumption that the observations are strictly...

We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible autoregressive moving-average (ARMA) time series models, which were initially established by Hannan [Journal of Applied Probability (1973) vol. 10, pp....

Hall & Yao (2003) showed that, for ARCH/GARCH, i.e. autoregressive conditional heteroscedastic/generalised autoregressive conditional heteroscedastic, models with heavy‐tailed errors, the conventional maximum quasilikelihood estimator suffers from complex limit distributions and slow...

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 provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible ARMA time series models, which were initially established by Hannan (1973) via the asymptotic properties of a Whittle's estimator. This also paves the way to...

This paper examines the Gaussian maximum likelihood estimator (GMLE) in the context of a general form of spatial autoregressive and moving average (ARMA) processes with finite second moment. The ARMA processes are supposed to be causal and invertible under the half-plane unilateral order, but...

The local linear regression technique is applied to estimation of functional-coefficient regression models for time series data. The models include threshold autoregressive models and functional-coefficient autoregressive models as special cases but with the added advantages such as depicting...