Smooth LASSO estimator for the function-on-function

An exploratory penalized regression to identify combined effects of temporal variables-application to agri-environmental issues

The development of sensors is opening new avenues in several fields of activity. Concerning agricultural crops, complex combinations of agri-environmental dynamics, such as soil and climate variables, are now commonly recorded. These new kinds of measurements are an opportunity to improve knowledge of the drivers of crop yield and crop quality at harvest. This involves renewing statistical approaches to account for the combined variations of these dynamic variables, here considered as temporal variables. The objective of the paper is to estimate an interpretable model to study the influence of the two combined inputs on a scalar output. A Sparse and Structured Procedure is proposed to Identify Combined Effects of Formatted temporal Predictors, hereafter denoted S piceFP. The method is based on the transformation of both temporal variables into categorical variables by defining joint modalities, from which a collection of multiple regression models is then derived. The regressors are the frequencies associated with joint class intervals. The class intervals and related regression coefficients are determined using a generalized fused lasso. S piceFP is a generic and exploratory approach. The simulations we performed show that it is flexible enough to select the non-null or influential modalities of values. A motivating example for grape quality is presented.

Adaptive LASSO estimation for functional hidden dynamic geostatistical models

We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hidden dynamic geostatistical models (f-HDGM). These models employ a classic mixed-effect regression structure with embedded spatiotemporal dynamics to model georeferenced data observed in a functional domain. Thus, the regression coefficients are functions. The algorithm simultaneously selects the relevant spline basis functions and regressors that are used to model the fixed effects. In this way, it automatically shrinks to zero irrelevant parts of the functional coefficients or the entire function for an irrelevant regressor. The algorithm is based on an adaptive LASSO penalty function, with weights obtained by the unpenalised f-HDGM maximum likelihood estimators. The computational burden of maximisation is drastically reduced by a local quadratic approximation of the log-likelihood. A Monte Carlo simulation study provides insight in prediction ability and parameter estimate precision, considering increasing spatiotemporal dependence and cross-correlations among predictors. Further, the algorithm behaviour is investigated when modelling air quality functional data with several weather and land cover covariates. Within this application, we also explore some scalability properties of our algorithm. Both simulations and empirical results show that the prediction ability of the penalised estimates are equivalent to those provided by the maximum likelihood estimates. However, adopting the so-called one-standard-error rule, we obtain estimates closer to the real ones, as well as simpler and more interpretable models.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00477-023-02466-5.