Superconsistent Estimation of Points of Impact in Non-Parametric Regression with Functional Predictors
| Autor: | Dominik Poß, Alois Kneip, Hedwig Eisenbarth, Lisa Feldman Barrett, Tor D. Wager, Dominik Liebl |
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| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Generalized linear model Variable selection Mathematics - Statistics Theory Sample (statistics) Statistics Theory (math.ST) 01 natural sciences Methodology (stat.ME) 010104 statistics & probability 03 medical and health sciences Statistics FOS: Mathematics Emotional stimuli 0101 mathematics Non‐parametric regression Statistics - Methodology 030304 developmental biology Mathematics 0303 health sciences ddc:519 Quasi‐maximum‐likelihood Functional data analysis Estimator State (functional analysis) On‐line video rating Outcome (probability) Nonparametric regression Rate of convergence Statistics Probability and Uncertainty |
| Zdroj: | Journal of the Royal Statistical Society Series B: Statistical Methodology. 82:1115-1140 |
| ISSN: | 1467-9868 1369-7412 |
| DOI: | 10.1111/rssb.12386 |
| Popis: | Summary Predicting scalar outcomes by using functional predictors is a classical problem in functional data analysis. In many applications, however, only specific locations or time points of the functional predictors have an influence on the outcome. Such ‘points of impact’ are typically unknown and must be estimated in addition to estimating the usual model components. We show that our points-of-impact estimator enjoys a superconsistent rate of convergence and does not require knowledge or pre-estimates of the unknown model components. This remarkable result facilitates the subsequent estimation of the remaining model components as shown in the theoretical part, where we consider the case of non-parametric models and the practically relevant case of generalized linear models. The finite sample properties of our estimators are assessed by means of a simulation study. Our methodology is motivated by data from a psychological experiment in which the participants were asked to rate their emotional state continuously while watching an affective video eliciting a varying intensity of emotional reactions. |
| Databáze: | OpenAIRE |
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