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Nonparametric inference in small data sets of spatially indexed curves with application to ionospheric trend determination

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  • Gromenko, Oleksandr
  • Kokoszka, Piotr

Abstract

This paper is concerned with estimation and testing in data sets consisting of a small number (about 20–30) of curves observed at unevenly distributed spatial locations. Such data structures may be referred to as spatially indexed functional data. Motivated by an important space physics problem, we model such data as a mean function plus spatially dependent error functions. Given a small number of spatial locations, the parametric methods for the estimation of the spatial covariance structure of the error functions are not satisfactory. We propose a fully nonparametric estimator for the mean function. We also derive a test to determine the significance of the regression coefficients if the mean function is a linear combination of known covariate functions. In particular, we develop methodology for the estimation a trend in spatially indexed functional data, and for assessing its statistical significance. We apply the new tools to global ionosonde records to test the hypothesis of ionospheric cooling. Nonparametric modeling of the space–time covariances is surprisingly simple, much faster than those previously proposed, and less sensitive to computational errors. In simulated data, the new estimator and test uniformly dominate those based on parametric modeling.

Suggested Citation

  • Gromenko, Oleksandr & Kokoszka, Piotr, 2013. "Nonparametric inference in small data sets of spatially indexed curves with application to ionospheric trend determination," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 82-94.
    • Handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:82-94
    DOI: 10.1016/j.csda.2012.09.016
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    References listed on IDEAS

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    1. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    2. Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
    3. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
    4. Adrian W. Bowman & Marco Giannitrapani & E. Marian Scott, 2009. "Spatiotemporal smoothing and sulphur dioxide trends over Europe," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(5), pages 737-752, December.
    5. Matthias Katzfuss & Noel Cressie, 2011. "Spatio‐temporal smoothing and EM estimation for massive remote‐sensing data sets," Journal of Time Series Analysis, Wiley Blackwell, vol. 32, pages 430-446, July.
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    Cited by:

    1. Mengchen Wang & Trevor Harris & Bo Li, 2023. "Asynchronous Changepoint Estimation for Spatially Correlated Functional Time Series," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 157-176, March.
    2. Kehui Chen & Pedro Delicado & Hans-Georg Müller, 2017. "Modelling function-valued stochastic processes, with applications to fertility dynamics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 177-196, January.
    3. Oleksandr Gromenko & Piotr Kokoszka & Matthew Reimherr, 2017. "Detection of change in the spatiotemporal mean function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 29-50, January.
    4. 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.
    5. Lin Zhang & Veerabhadran Baladandayuthapani & Hongxiao Zhu & Keith A. Baggerly & Tadeusz Majewski & Bogdan A. Czerniak & Jeffrey S. Morris, 2016. "Functional CAR Models for Large Spatially Correlated Functional Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 772-786, April.
    6. Jingjing Yang & Dennis D. Cox & Jong Soo Lee & Peng Ren & Taeryon Choi, 2017. "Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian–Wishart processes," Biometrics, The International Biometric Society, vol. 73(4), pages 1082-1091, December.
    7. Burdejova, P. & Härdle, W. & Kokoszka, P. & Xiong, Q., 2017. "Change point and trend analyses of annual expectile curves of tropical storms," Econometrics and Statistics, Elsevier, vol. 1(C), pages 101-117.

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