Some Recent Developments in Inference for Geostatistical Functional Data

We review recent developments related to inference for functions defined at spatial locations. We also consider time series of functions defined at irregularly distributed spatial points or on a grid. We focus on kriging, estimation of the functional mean and principal components, and significance testing, giving special attention to testing spatio--temporal separability in the context of functional data. We also highlight some ideas related to extreme value theory for spatially indexed functional time series.

[1]  Raymond G. Roble,et al.  How will changes in carbon dioxide and methane modify the mean structure of the mesosphere and thermosphere , 1989 .

[2]  Surajit Ray,et al.  Functional principal component analysis of spatially correlated data , 2014, Stat. Comput..

[3]  Piotr Kokoszka,et al.  Quantifying the risk of heat waves using extreme value theory and spatio-temporal functional data , 2019, Comput. Stat. Data Anal..

[4]  Piotr Kokoszka,et al.  Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends , 2012, 1206.6655.

[5]  A. Gelfand,et al.  Handbook of spatial statistics , 2010 .

[6]  Piotr Kokoszka,et al.  Nonparametric inference in small data sets of spatially indexed curves with application to ionospheric trend determination , 2013, Comput. Stat. Data Anal..

[7]  M. Sherman.  Spatial Statistics and Spatio-Temporal Data: Covariance Functions and Directional Properties , 2010 .

[8]  J. Teugels,et al.  Statistics of Extremes , 2004 .

[9]  Piotr Kokoszka,et al.  Detection of change in the spatiotemporal mean function , 2017 .

[10]  Jorge Mateu,et al.  Statistics for spatial functional data: some recent contributions , 2009 .

[11]  Piotr Kokoszka,et al.  Inference for Functional Data with Applications , 2012 .

[12]  P. Kokoszka,et al.  Introduction to Functional Data Analysis , 2017 .

[13]  Jorge Mateu,et al.  A universal kriging approach for spatial functional data , 2013, Stochastic Environmental Research and Risk Assessment.

[14]  P. Kokoszka,et al.  Testing separability of space--time functional processes , 2015, 1509.07017.

[15]  Alessandra Menafoglio,et al.  A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space , 2013 .

[16]  L. Horváth,et al.  Limit Theorems in Change-Point Analysis , 1997 .

[17]  John A. D. Aston,et al.  Tests for separability in nonparametric covariance operators of random surfaces , 2015, 1505.02023.

[18]  M. Genton,et al.  A likelihood ratio test for separability of covariances , 2006 .

[19]  H. Rishbeth,et al.  A greenhouse effect in the ionosphere , 1990 .

[20]  Piotr Kokoszka,et al.  Evaluation of the cooling trend in the ionosphere using functional regression with incomplete curves , 2017 .

[21]  P. Kokoszka,et al.  Consistency of the mean and the principal components of spatially distributed functional data , 2013 .

[22]  D. Zimmerman,et al.  The likelihood ratio test for a separable covariance matrix , 2005 .

[23]  Multivariate Geostatistics , 2004 .

[24]  Carol A. Gotway,et al.  Statistical Methods for Spatial Data Analysis , 2004 .