Regression models to relate a scalar Y to a functional predictor X(t) are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, β(t), with Y related to X(t) through ∫ β(t)X(t) dt . Regions where β(t) = 0 correspond to places where there is a relationship between X(t) and Y . Alternatively, points where β(t)= 0 indicate no relationship. Hence, for...

sional realization theory," &YAM J. Cone., vol. 13, pp. 221-241, Jan. 1965. H. J. Sussmann, "Existence and uniqueness of minimal realizations of nonlinear systems-Part I: Initialized systems," J. Math. Syst. Theory, t o be published. , "Orbits of families of vector fields and integrability of systems with singularities," Bull. Amer. Math. Soc., vol. 79, pp. 197-199, 1973. P. Stefan, "Two proofs...

We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronized penalization. An asymptotic expansion of the mean square prevision error is given. The model and the...

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical interest in the slope centers on its application for the purpose of prediction, rather than on its significance in its own right. We show that the problems of slope...

NCSU, Princeton University, and UC-Davis Abstract: Functional linear regression analysis aims to model regression relations which include a functional predictor. The analogue to the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression models is a regression parameter function in one or two arguments. If in addition one has scalar predictors, ...

In this second chapter on the functional linear model, the dependent or response variable is functional. We first consider a situation in which all of the independent variables are scalar and in particular look at two functional analyses of variance. When one or more of the independent variables is also function, we have two possible classes of linear models. The simpler case is called concurre...