Nonparametric inference in small data sets of spatially indexed curves with application to ionospheric trend determination
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- LÃ³pez-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.
- 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.
- Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
- 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, 07.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:82-94. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.