This paper describes a wavelet method for the estimation of density and hazard rate functions from randomly right censored data. We adopt a nonparametric approach in assuming that the density and hazard rate have no speciic parametric form. The method is based on dividing the time axis into a dyadic number of intervals and then counting the number of events… (More)
Many time series are not second-order stationary and it is not appropriate to analyze them using methods designed for stationary series. This article introduces a new test for second-order stationarity that detects different kinds of departures from stationarity than those based on Fourier methods. The new test is also computationally fast, designed to work… (More)
SUMMARY This article is about using cross-validation in conjunction with the Kovac-Silverman in-terpolatory algorithm for wavelet shrinkage.
SUMMARY The development and usage of a three-dimensional projection pursuit software package is discussed. The well-established Jones and Sibson moments index is chosen as a computationally efficient projection index to extend to 3D. Computer algebraic methods are extensively employed to handle the long and complex formulae that constitute the index and are… (More)
This paper introduces an image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform. Both the minimal (unitary) and redundant (maximum overlap) versions of the transform are used. The covariance structure of white noise in wavelet domain is established. Estimation is performed via empirical Bayesian techniques, including versions… (More)
It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet spectrum of a locally stationary wavelet time series. Our new method works by combining the advantages of a Haar-Fisz… (More)
Prévision non paramétrique de processus à valeurs fonctionnelles. Résumé Nous traitons dans cette thèse le problème de la prédiction d'un processus stochastique à valeurs fonctionnelles. Nous commençons par étudier le modèle proposé par Antoniadis et al. (2006) dans le cadre d'une application pratique-la demande d'énergie électrique en France-où l'hypothèse… (More)
—We apply a non-parametric regression technique based on second generation wavelets to irregularly spaced network data. Conventional wavelet based non-parametric regression can be modelled as, f i = gi +i, where fi = f (ti), gi = g(ti) and i = 1, ..., n. Key requirements for this model are that n = 2 J for some J ∈ N, data are observed on a regular grid ti… (More)