This paper considers parameter estimation for nonlinear and non-Gaussian state-space models with correlation. We propose an asymptotic quasilikelihood (AQL) approach which utilises a nonparametric kernel estimator of the conditional variance covariances matrix Σt to replace the true Σt in the standard quasi-likelihood. The kernel estimation avoids the risk of potential miss-specification of Σt ...

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an “equivalent” reproducing kernel regression estimator, as well as for proving uniform error bounds on the reproducing kernel regre...

Suppose we want to estimate a density at a point where we know the values of its first or higher order derivatives. In this case a given kernel estimator of the density can be modified by adding appropriately weighted kernel estimators of these derivatives. We give conditions under which the modified estimators are asymptotically normal. We also determine the optimal weights. When the highest d...

Statistical modeling of physical laws connects experiments with mathematical descriptions of natural phenomena. The modeling is based on the probability density of measured variables expressed by experimental data via a kernel estimator. As an objective kernel the scattering function determined by calibration of the instrument is introduced. This function provides for a new definition of experi...

This paper develops a robust testing procedure for the nonparametric kernel method in the presence of temporal dependence of unknown forms. We …rst propose a new variance estimator that corrects the …nite sample bias caused by temporal dependence. The new variance estimator is novel in the sense that it is not only robust to temporal dependence in …nite samples but also consistent in large samp...