Regression when both response and predictor are functions

Quantile regression when the covariates are functions

This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a penalized L type criterion. Then, we study the asymptotic behavior of this estimator. The penalization is of primary importance to get existence and convergence.

Recursive Path Models when Both Predictor and Response Variables are Categorical

Recursive path analysis is a useful tool for inference on a sequence of three or more response variables in which the causal effects of variables, if any, are in one direction. The primary objective in such analysis is to decompose the total effect of each variable into its direct and indirect components. Methods for recursive analysis of a chain of continuous variables are well developed but t...

When are Borel functions Baire functions ?

The following two theorems give the flavour of what will be proved. THEOREM. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0, 1] to Y coincide if and only if Y is connected and locally connected. THEOREM. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class fun...

Of Politicians and Technocrats, and Why Global Health Scholars Are Inevitably a Bit of Both: A Response to Recent Commentaries

When the Data Are Functions

A datum is often a continuous function x(t) of a variable such as time observed over some interval. One or more such functions are observed for each subject or unit of observation. The extension of classical data analytic techniques designed for p-variate observations to such data is discussed. The essential step is the expression of the classical problem in the language of functional analysis,...