Pr{\'e}diction optimale pour un mod{\`e}le ordinal {\`a} covariables fonctionnelles

TL;DR

This paper develops an optimal prediction framework for ordinal models with functional covariates, reformulating them into scalar models and illustrating their application with a real dataset for connected glasses.

Contribution

It introduces explicit optimal prediction methods for ordinal models with functional covariates and reformulates such models into scalar covariate models.

Findings

Explicit form of Least-Absolute-Deviation prediction for ordinal models

Reformulation of functional covariate models into scalar covariate models

Application to real dataset for connected glasses control

Abstract

We present a prediction framework for ordinal models: we introduce optimal predictions using loss functions and give the explicit form of the Least-Absolute-Deviation prediction for these models. Then, we reformulate an ordinal model with functional covariates to a classic ordinal model with multiple scalar covariates. We illustrate all the proposed methods and try to apply these to a dataset collected by EssilorLuxottica for the development of a control algorithm for the shade of connected glasses.