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Superconsistent estimation of points of impact in non‐parametric regression with functional predictors

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  • Dominik Poß
  • Dominik Liebl
  • Alois Kneip
  • Hedwig Eisenbarth
  • Tor D. Wager
  • Lisa Feldman Barrett

Abstract

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.

Suggested Citation

  • Dominik Poß & Dominik Liebl & Alois Kneip & Hedwig Eisenbarth & Tor D. Wager & Lisa Feldman Barrett, 2020. "Superconsistent estimation of points of impact in non‐parametric regression with functional predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 1115-1140, September.
    • Handle: RePEc:bla:jorssb:v:82:y:2020:i:4:p:1115-1140
    DOI: 10.1111/rssb.12386
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    References listed on IDEAS

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    1. Lindquist, Martin A. & McKeague, Ian W., 2009. "Logistic Regression With Brownian-Like Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1575-1585.
    2. Michael E. Sobel & Martin A. Lindquist, 2014. "Causal Inference for fMRI Time Series Data With Systematic Errors of Measurement in a Balanced On/Off Study of Social Evaluative Threat," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 967-976, September.
    3. Berrendero, José R. & Bueno-Larraz, Beatriz & Cuevas, Antonio, 2019. "An RKHS model for variable selection in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 25-45.
    4. Lee, Charles M C & Ready, Mark J, 1991. "Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-746, June.
    5. Boente, Graciela & Salibián Barrera, Matías & Tyler, David E., 2014. "A characterization of elliptical distributions and some optimality properties of principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 254-264.
    6. Aneiros, Germán & Vieu, Philippe, 2014. "Variable selection in infinite-dimensional problems," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 12-20.
    7. Floriello, Davide & Vitelli, Valeria, 2017. "Sparse clustering of functional data," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 1-18.
    8. Martin A. Lindquist, 2012. "Functional Causal Mediation Analysis With an Application to Brain Connectivity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1297-1309, December.
    9. John K. Dagsvik & Steinar StrØm, 2006. "Sectoral labour supply, choice restrictions and functional form," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 803-826, September.
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