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A Modified Neighborhood Hypothesis Test for Population Mean in Functional Data

Author

Listed:
  • Dhanamalee Bandara

    (University of Wisconsin-Green Bay)

  • Leif Ellingson

    (Texas Tech University)

  • Souparno Ghosh

    (University of Nebraska-Lincoln)

  • Ranadip Pal

    (Texas Tech University)

Abstract

When dealing with very high-dimensional and functional data, rank deficiency of sample covariance matrix often complicates the tests for population mean. To alleviate this rank deficiency problem, Munk et al. (J Multivar Anal 99:815–833, 2008) proposed neighborhood hypothesis testing procedure that tests whether the population mean is within a small, pre-specified neighborhood of a known quantity, M. How could we objectively specify a reasonable neighborhood, particularly when the sample space is unbounded? What should be the size of the neighborhood? In this article, we develop the modified neighborhood hypothesis testing framework to answer these two questions. We define the neighborhood as a proportion of the total amount of variation present in the population of functions under study and proceed to derive the asymptotic null distribution of the appropriate test statistic. Power analyses suggest that our approach is appropriate when sample space is unbounded and is robust against error structures with nonzero mean. We then apply this framework to assess whether the near-default sigmoidal specification of dose-response curves is adequate for widely used CCLE database. Results suggest that our methodology could be used as a pre-processing step before using conventional efficacy metrics, obtained from sigmoid models (for example: IC $$_{50}$$ 50 or AUC), as downstream predictive targets.

Suggested Citation

  • Dhanamalee Bandara & Leif Ellingson & Souparno Ghosh & Ranadip Pal, 2024. "A Modified Neighborhood Hypothesis Test for Population Mean in Functional Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(1), pages 1-18, March.
  • Handle: RePEc:spr:jagbes:v:29:y:2024:i:1:d:10.1007_s13253-023-00549-y
    DOI: 10.1007/s13253-023-00549-y
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    References listed on IDEAS

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    1. Ellingson, Leif & Patrangenaru, Vic & Ruymgaart, Frits, 2013. "Nonparametric estimation of means on Hilbert manifolds and extrinsic analysis of mean shapes of contours," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 317-333.
    2. Jordi Barretina & Giordano Caponigro & Nicolas Stransky & Kavitha Venkatesan & Adam A. Margolin & Sungjoon Kim & Christopher J.Wilson & Joseph Lehár & Gregory V. Kryukov & Dmitriy Sonkin & Anupama Red, 2012. "Addendum: The Cancer Cell Line Encyclopedia enables predictive modelling of anticancer drug sensitivity," Nature, Nature, vol. 492(7428), pages 290-290, December.
    3. Jordi Barretina & Giordano Caponigro & Nicolas Stransky & Kavitha Venkatesan & Adam A. Margolin & Sungjoon Kim & Christopher J. Wilson & Joseph Lehár & Gregory V. Kryukov & Dmitriy Sonkin & Anupama Re, 2012. "The Cancer Cell Line Encyclopedia enables predictive modelling of anticancer drug sensitivity," Nature, Nature, vol. 483(7391), pages 603-607, March.
    4. Munk, A. & Paige, R. & Pang, J. & Patrangenaru, V. & Ruymgaart, F., 2008. "The one- and multi-sample problem for functional data with application to projective shape analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 815-833, May.
    5. Qian Wan & Ranadip Pal, 2014. "An Ensemble Based Top Performing Approach for NCI-DREAM Drug Sensitivity Prediction Challenge," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-12, June.
    6. Zhaleh Safikhani & Petr Smirnov & Kelsie L. Thu & Jennifer Silvester & Nehme El-Hachem & Rene Quevedo & Mathieu Lupien & Tak W. Mak & David Cescon & Benjamin Haibe-Kains, 2017. "Gene isoforms as expression-based biomarkers predictive of drug response in vitro," Nature Communications, Nature, vol. 8(1), pages 1-11, December.
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