Consistency of the Mean and the Principal Components of Spatially Distributed Functional Data
This paper develops a framework for the estimation of the functionalmean and the functional principal componentswhen the functions form a random field.We establish conditions for the sample average (in space) to be a consistent estimator of the population mean function, and for the usual empirical covariance operator to be a consistent estimator of the population covariance operator.
KeywordsGene Expression Pattern Recognition Stochastic Process Probability Theory Computer Image
Unable to display preview. Download preview PDF.
- 1.Hörmann, S., Kokoszka, P.: Consistency of the mean and the principal components of spatially distributed functional data. Submitted (2011)Google Scholar
- 2.Lahiri, S.N.: On the inconsistency of estimators based on spatial data under infill asymptotics. Sankhy¯a Ser. A, 58, 403–417 (1996)Google Scholar
- 3.Lahiri, S.N.: Central limit theorems for weighted sums of a spatial process under a class of stochastic and fixed designs. Sankhy¯a Ser. A, 65, 356–388 (2003)Google Scholar
- 4.Park, B.U., Kim, T.Y., Park, J-S., Hwang, S.Y.: Practically applicable central limit theorems for spatial statistics. Mathematical Geosciences, 41, 555–569 (2009)Google Scholar
- 5.Ramsay, J.O. and Silverman, B.W.: Functional Data Analysis. Springer, New York (2005)Google Scholar
- 6.Rio, E.: Covariance inequalities for strongly mixing processes. Ann. Inst. H. Poincar´e Probab. Statist., 29, 587–597 (1993)Google Scholar