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Switching nonparametric regression models for multi-curve data
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Switching nonparametric regression models for multi-curve data
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Switching nonparametric regression models for multi-curve data
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Journal Article
Switching nonparametric regression models for multi-curve data
2017
Overview
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to “switch” from one function to another. Thus each curve follows what we call a switching nonparametric regression model. We develop an EM algorithm to estimate the model parameters. We also obtain standard errors for the parameter estimates of the state process. We consider three types of hidden states: those that are independent and identically distributed, those that follow a Markov structure, and those that are independent but with distribution depending on some covariate(s). A simulation study shows the frequentist properties of our estimates. We apply our methods to a building’s power usage data.
Les auteures développent et mettent en application une approche d’analyse de données multicourbes où chaque courbe est générée par un processus latent. L’état d’un point particulier détermine une fonction lisse, forçnt les courbes individuelles à passer d’une fonction à l’autre. Chaque courbe suit ainsi ce que les auteures appellent un modèle de régression non paramétrique intermittent. Elles développent un algorithme EM pour estimer les paramètres et obtiennent les erreur-types pour les estimateurs des paramètres du modèle d’états. Les auteures considèrent trois types d’états cachés: ceux qui sont indépendants et identiquement distribués, ceux qui suivent une structure de Markov, et ceux qui sont indépendants mais dont la distribution dépend de covariables. Elles présentent une simulation afin de montrer les propriétés fréquentistes de leurs estimateurs et appliquent leur méthode à des données réelles de consommation d’énergie de bâtiments.
