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Functional Wavelet-Based Modelling of Dependence Between Lupus and Stress

Author

Listed:
  • Ana M. Aguilera

    (University of Granada)

  • Manuel Escabias

    (University of Granada)

  • Francisco A. Ocaña

    (University of Granada)

  • Mariano J. Valderrama

    (University of Granada)

Abstract

The power of functional linear regression to estimate a set of curves from others involved is studied in this work in the context of life sciences. The objective is to determine the relationship between the degree of lupus and the level of stress for patients suffering this autoimmune disease. Daily stress and lupus curves have a strong local behavior with missing data those days that a patient does not answer the corresponding test. Because of this, wavelet smoothing with an appropriate thresholding rule is considered. Then, functional principal component analysis of the response and predictor variables is used to reduce the dimension and solve the multicollinearity problem that affects the estimation of the functional linear regression model with functional response. Model selection is solved by using a criterion that selects those pairs of response/predictor components that explain the highest proportions of response variability. The performance of the proposed functional model is tested on simulated and real data.

Suggested Citation

  • Ana M. Aguilera & Manuel Escabias & Francisco A. Ocaña & Mariano J. Valderrama, 2015. "Functional Wavelet-Based Modelling of Dependence Between Lupus and Stress," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 1015-1028, December.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-014-9424-5
    DOI: 10.1007/s11009-014-9424-5
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    References listed on IDEAS

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    1. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    2. Mariano J. Valderrama & Francisco A. Ocaña & Ana M. Aguilera & Francisco M. Ocaña-Peinado, 2010. "Forecasting Pollen Concentration by a Two-Step Functional Model," Biometrics, The International Biometric Society, vol. 66(2), pages 578-585, June.
    3. M. Aguilera-Morillo & Ana Aguilera & Manuel Escabias & Mariano Valderrama, 2013. "Penalized spline approaches for functional logit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 251-277, June.
    4. Ana Aguilera & Francisco Ocaña & Mariano Valderrama, 1999. "Forecasting with unequally spaced data by a functional principal component approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 233-253, June.
    5. Aguilera, Ana M. & Escabias, Manuel & Valderrama, Mariano J., 2008. "Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 151-163, September.
    6. Francisco Ocaña & Ana Aguilera & Manuel Escabias, 2007. "Computational considerations in functional principal component analysis," Computational Statistics, Springer, vol. 22(3), pages 449-465, September.
    7. Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
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    Cited by:

    1. 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.
    2. Aguilera-Morillo, M. Carmen & Aguilera, Ana M. & Jiménez-Molinos, Francisco & Roldán, Juan B., 2019. "Stochastic modeling of Random Access Memories reset transitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 197-209.

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