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Estimation, imputation and prediction for the functional linear model with scalar response with responses missing at random

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  • Febrero-Bande, Manuel
  • Galeano, Pedro
  • González-Manteiga, Wenceslao

Abstract

Two different methods for estimation, imputation and prediction for the functional linear model with scalar response when some of the responses are missing at random (MAR) are developed. The simplified method consists in estimating the model parameters using only the pairs of predictors and responses observed completely. In addition the imputed method consists in estimating the model parameters using both the pairs of predictors and responses observed completely and the pairs of predictors and responses imputed with the parameters estimated with the simplified method. The two methodologies are compared in an extensive simulation study and the analysis of two real data examples. The comparison provides evidence that the imputed method might have better performance than the simplified method if the numbers of functional principal components used in the former strategy are selected appropriately.

Suggested Citation

  • Febrero-Bande, Manuel & Galeano, Pedro & González-Manteiga, Wenceslao, 2019. "Estimation, imputation and prediction for the functional linear model with scalar response with responses missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 91-103.
    • Handle: RePEc:eee:csdana:v:131:y:2019:i:c:p:91-103
    DOI: 10.1016/j.csda.2018.07.006
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    1. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
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    7. Manuel Febrero-Bande & Pedro Galeano & Wenceslao González-Manteiga, 2017. "Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study," International Statistical Review, International Statistical Institute, vol. 85(1), pages 61-83, April.
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    Cited by:

    1. Antonio Elías & Raúl Jiménez & J. E. Yukich, 2023. "Localization processes for functional data analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 485-517, June.
    2. Christian Acal & Manuel Escabias & Ana M. Aguilera & Mariano J. Valderrama, 2021. "COVID-19 Data Imputation by Multiple Function-on-Function Principal Component Regression," Mathematics, MDPI, vol. 9(11), pages 1-23, May.
    3. Nengxiang Ling & Lilei Cheng & Philippe Vieu & Hui Ding, 2022. "Missing responses at random in functional single index model for time series data," Statistical Papers, Springer, vol. 63(2), pages 665-692, April.
    4. Jorge R. Sosa Donoso & Miguel Flores & Salvador Naya & Javier Tarrío-Saavedra, 2023. "Local Correlation Integral Approach for Anomaly Detection Using Functional Data," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    5. Manuel Febrero-Bande & Pedro Galeano & Eduardo García-Portugués & Wenceslao González-Manteiga, 2024. "Testing for linearity in scalar-on-function regression with responses missing at random," Computational Statistics, Springer, vol. 39(6), pages 3405-3429, September.

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