Two dimensional reduction regression methods to predict a scalar response from a discretized sample path of a continuous time covariate process are presented. The methods take into account the functional nature of the predictor and are both based on appropriate wavelet decompositions. Using such decompositions, we derive prediction methods that are similar to minimum average variance estimation...

In this paper, a statistical method is proposed to evaluate the 4 physical properties of surface materials on Mars from hyperspectral images 5 collected by the OMEGA instrument aboard the Mars express spacecraft. 6 The approach is based on the estimation of the functional relationship F be-7 tween some observed spectra and some physical parameters. To this end, a 8 database of synthetic spectra...

Methods of dimension reduction are very helpful and almost a necessity if we want to analyze high-dimensional time series since otherwise modelling affords many parameters because of interactions at various time-lags. We use a dynamic version of Sliced Inverse Regression (SIR; Li (1991)), which was developed to reduce the dimension of the regressor in regression problems, as an exploratory tool...

Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is, when the dimension of the covariat...

Sliced inverse regression and principal Hessian directions (Li, 1991, 1992) aim to reduce the dimensionality of regression problems. An important step in the method is the determination of a suitable dimension. While statistical tests based on the nullity eigenvalues are usually suggested, we here focus on the quality of the estimation of the eeective dimension reduction (edr) spaces. Essential...

The estimation of nonlinear functions can be challenging when the number of independent variables is high. This difficulty may, in certain cases, be reduced by first projecting the independent variables on a lower dimensional subspace before estimating the nonlinearity. In this paper, a statistical nonparametric dimension reduction method called sliced inverse regression is presented and a cons...