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High-dimensional adaptive function-on-scalar regression

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  • Fan, Zhaohu
  • Reimherr, Matthew

Abstract

Applications of functional data with large numbers of predictors have grown precipitously in recent years, driven, in part, by rapid advances in genotyping technologies. Given the large numbers of genetic mutations encountered in genetic association studies, statistical methods which more fully exploit the underlying structure of the data are imperative for maximizing statistical power. However, there is currently very limited work in functional data with large numbers of predictors. Tools are presented for simultaneous variable selection and parameter estimation in a functional linear model with a functional outcome and a large number of scalar predictors; the technique is called AFSL for Adaptive Function-on-Scalar Lasso. It is demonstrated how techniques from convex analysis over Hilbert spaces can be used to establish a functional version of the oracle property for AFSL over any real separable Hilbert space, even when the number of predictors, I, is exponentially large compared to the sample size, N. AFSL is illustrated via a simulation study and data from the Childhood Asthma Management Program, CAMP, selecting those genetic mutations which are important for lung growth.

Suggested Citation

  • Fan, Zhaohu & Reimherr, Matthew, 2017. "High-dimensional adaptive function-on-scalar regression," Econometrics and Statistics, Elsevier, vol. 1(C), pages 167-183.
    • Handle: RePEc:eee:ecosta:v:1:y:2017:i:c:p:167-183
    DOI: 10.1016/j.ecosta.2016.08.001
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
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    5. Reiss Philip T. & Huang Lei & Mennes Maarten, 2010. "Fast Function-on-Scalar Regression with Penalized Basis Expansions," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-30, August.
    6. Matthew Reimherr & Dan Nicolae, 2016. "Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 407-422, March.
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    Cited by:

    1. Jiang Du & Hui Zhao & Zhongzhan Zhang, 2019. "Dynamic partially functional linear regression model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 679-693, December.
    2. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Mirshani, Ardalan & Reimherr, Matthew, 2021. "Adaptive function-on-scalar regression with a smoothing elastic net," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Craig, Sarah J.C. & Kenney, Ana M. & Lin, Junli & Paul, Ian M. & Birch, Leann L. & Savage, Jennifer S. & Marini, Michele E. & Chiaromonte, Francesca & Reimherr, Matthew L. & Makova, Kateryna D., 2023. "Constructing a polygenic risk score for childhood obesity using functional data analysis," Econometrics and Statistics, Elsevier, vol. 25(C), pages 66-86.
    5. Kokoszka, Piotr & Oja, Hanny & Park, Byeong & Sangalli, Laura, 2017. "Special issue on functional data analysis," Econometrics and Statistics, Elsevier, vol. 1(C), pages 99-100.
    6. Qin, Yichen & Wang, Linna & Li, Yang & Li, Rong, 2023. "Visualization and assessment of model selection uncertainty," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    7. Ghosal, Rahul & Ghosh, Sujit & Urbanek, Jacek & Schrack, Jennifer A. & Zipunnikov, Vadim, 2023. "Shape-constrained estimation in functional regression with Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    8. Xie, Haihan & Kong, Linglong, 2023. "Gaussian copula function-on-scalar regression in reproducing kernel Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

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