Wavelet Deconvolution in a Periodic Setting with Long-Range Dependent Errors

In this paper, a hard thresholding wavelet estimator is constructed for a deconvolution model in a periodic setting that has long-range dependent noise. The estimation paradigm is based on a maxiset method that attains a near optimal rate of convergence for a variety of L_p loss functions and a wide variety of Besov spaces in the presence of strong dependence. The effect of long-range dependence is detrimental to the rate of convergence. The method is implemented using a modification of the WaveD-package in R and an extensive numerical study is conducted. The numerical study supplements the theoretical results and compares the LRD estimator with na\"ively using the standard WaveD approach

Kink estimation in stochastic regression with dependent errors and predictors

In this article we study the estimation of the location of jump points in the first derivative (referred to as kinks) of a regression function \mu in two random design models with different long-range dependent (LRD) structures. The method is based on the zero-crossing technique and makes use of high-order kernels. The rate of convergence of the estimator is contingent on the level of dependence and the smoothness of the regression function \mu. In one of the models, the convergence rate is the same as the minimax rate for kink estimation in the fixed design scenario with i.i.d. errors which suggests that the method is optimal in the minimax sense.Comment: 35 page

Moped and motor scooter licensing and training: current approaches and future challenges

Unlike some European countries, there have been few motor scooters and mopeds on Australian roads and licensing and training of these riders has received little attention. However, recent increases in the sales of scooters (many of which are officially mopeds) have stimulated interest in how these vehicles can be best managed in Australia. This paper reviews local and international approaches to moped and motor scooter licensing and training, and seeks to assess their relevance to the current Australian situation. A number of challenges to developing a coherent licensing and training system are identified and discussed: lack of information regarding moped and motor scooter safety and about the safety outcomes of current licensing and training systems, the absence of official definitions of scooters worldwide, the significant growth in this market, whether different licensing and training requirements should apply to tourists, and the status of similar vehicles