We show how cubic smoothing splines fitted to univariate time series data can be used to obtain local linear forecasts. Our approach is based on a stochastic state space model which allows the use of a likelihood approach for estimating the smoothing parameter, and which enables easy...

We provide Markov chain Monte Carlo (MCMC) algorithms for computing the bandwidth matrix for multivariate kernel density estimation. Our approach is based on treating the elements of the bandwidth matrix as parameters to be estimated, which we do by optimizing the likelihood cross-validation...

Multivariate kernel regression is an important tool for investigating the relationship between a response and a set of explanatory variables. It is generally accepted that the performance of a kernel regression estimator largely depends on the choice of bandwidth rather than the kernel function....

This paper aims to investigate a Bayesian sampling approach to parameter estimation in the semiparametric GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This...

We approximate the error density of a nonparametric regression model by a mixture of Gaussian densities with means being the individual error realizations and variance a constant parameter. We investigate the construction of a likelihood and posterior for bandwidth parameters under this...

Statistical models can play a crucial role in decision making. Traditional model validation tests typically make restrictive parametric assumptions about the model under the null and the alternative hypotheses. The majority of these tests examine one type of change at a time. This paper presents...