We consider the nonparametric regression model with long memory data that are not necessarily Gaussian and provide an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet-based mean regression function estimators. We show this MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel...

We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph’s trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by considering the Theil index, which is an established statistical measure used to determine levels of inequality across a system of ‘agents’, e.g., income lev...

A nonparametric kernel density estimator for directional–linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions for bias, variance and mean integrated square error (MISE) are derived, jointly with an asymptotic normality result for the proposed estimator. For some part...

Although there are many existing alternative methods for using structural characterizations of undirected graphs for embedding, clustering and classification problems, there is relatively little literature aimed at dealing with such problems for directed graphs. In this paper we present a novel method for characterizing graph structure that can be used to embed directed graphs into a feature sp...

In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [−1− √ 2,−2) and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [α1,−1− √ 2) where α1 is the smallest root(≈ −2.4812) of the polynomial x3 + 2x2 − 2x − 2. From these results, we ...

iv Acknowledgements v List of Tables vii List of Graphs vii