Aldo Goia

An introduction to recent advances in high/infinite dimensional statistics

Abstract The aim of this short contribution is to present the various papers composing this Special Issue on Statistics in HD spaces, by casting them into their bibliographical context through some necessarily short and selected discussion of the current literature.

Functional nonparametric model for time series: a fractal approach for dimension reduction

AbstracIn this paper we propose a functional nonparametric model for time series prediction. The originality of this model consists in using as predictor a continuous set of past values. This time series problem is presented in the general framework of regression estimation from dependent samples with regressor valued in some infinite dimensional semi-normed vectorial space. The curse of dimensionality induced by our approach is overridden by means of fractal dimension considerations. We give asymptotics for a kernel type nonparametric predictor linking the rates of convergence with the fractal dimension of the functional process. Finally, our method has been implemented and applied to some electricity consumption data.

Testing for No Effect in Functional Linear Regression Models, Some Computational Approaches

Abstract The functional linear regression model is a regression model where the link between the response (a scalar) and the predictor (a random function) is expressed as an inner product between a functional coefficient and the predictor. Our aim is to test at first for no effect of the model, i.e., the nullity of the functional coefficient. A fully automatic permutation test based on the cross covariance operator of the predictor and the response is proposed. The model can be, in an obvious way, extended to the case of several functional predictors. When testing for no effect of some covariate on the response the permutation test is no longer valid. An alternative pseudo-likelihood ratio test statistic is then introduced. The procedure can be applied in some way to test partial nullity of a functional coefficient. All procedures are illustrated and compared by means of simulation studies.

Classification methods for Hilbert data based on surrogate density

An unsupervised and a supervised classification approach for Hilbert random curves are studied. Both rest on the use of a surrogate of the probability density which is defined, in a distribution-free mixture context, from an asymptotic factorization of the small-ball probability. That surrogate density is estimated by a kernel approach from the principal components of the data. The focus is on the illustration of the classification algorithms and the computational implications, with particular attention to the tuning of the parameters involved. Some asymptotic results are sketched. Applications on simulated and real datasets show how the proposed methods work.

Some Insights About the Small Ball Probability Factorization for Hilbert Random Elements

Asymptotic factorizations for the small-ball probability (SmBP) of a Hilbert valued random element

Recent Advances on Functional Additive Regression

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Nonparametric Functional Methods: New Tools for Chemometric Analysis

are rigorously established and discussed. In particular, given the first

A new powerful version of the BUS test of normality

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Peak-Load Forecasting Using a Functional Semi-Parametric Approach

principal components (PCs) and as the radius

Describing the concentration of income populations by functional principal component analysis on Lorenz curves

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