We consider local smoothing of datasets where the design space is the d-dimensional (d>=1) torus and the response variable is real-valued. Our purpose is to extend least squares local polynomial fitting to this situation. We give both theoretical and empirical results.

We develop nonparametric smoothing for regression when both the predictor and the response variables are defined on a sphere of whatever dimension. A local polynomial fitting approach is pursued, which retains all the advantages in terms of rate optimality, interpretability, and ease of...

Measuring the quality of determined protein structures is a very important problem in bioinformatics. Kernel density estimation is a well-known nonparametric method which is often used for exploratory data analysis. Recent advances, which have extended previous linear methods to...

We introduce a class of excited random walks defined on trees. The transience on the supercritical Galton-Watson tree for some processes in this class is proved as well as a conjecture of [Volkov, S., 2003. Excited random walk on trees. Electronic Journal of Probability 8, 1-15] which is closely...

In certain multivariate problems the full probability density has an awkward normalizing constant, but the conditional and/or marginal distributions may be much more tractable. In this paper we investigate the use of composite likelihoods instead of the full likelihood. For closed exponential...

Given angular data [theta]1,...,[theta]n[set membership, variant][0,2[pi]) a common objective is to estimate the density. In case that a kernel estimator is used, bandwidth selection is crucial to the performance. A "plug-in rule" for the bandwidth, which is based on the concentration of a...

A Bayesian method for segmenting weed and crop textures is described and implemented. The work forms part of a project to identify weeds and crops in images so that selective crop spraying can be carried out. An image is subdivided into blocks and each block is modelled as a single texture. The...