Kernel spatial density estimation in infinite dimension space
- 330 Downloads
In this paper, we propose a nonparametric method to estimate the spatial density of a functional stationary random field. This latter is with values in some infinite dimensional normed space and admitted a density with respect to some reference measure. We study both the weak and strong consistencies of the considered estimator and also give some rates of convergence. Special attention is paid to the links between the probabilities of small balls and the rates of convergence of the estimator. The practical use and the behavior of the estimator are illustrated through some simulations and a real data application.
KeywordsDensity estimation Random fields Functional variables Infinite dimensional space Small balls probabilities Mixing conditions
Unable to display preview. Download preview PDF.
- Bar-Hen A, Bel L, Cheddadi R (2008) Spatio-temporal functional regression on paleoecological data. In: Dabo-Niang S, Ferraty F (eds) Functional and operatorial statistics. Springer, BerlinGoogle Scholar
- Bogachev V (1999) Gaussian measures(Math surveys and monographs). American Mathematical Society, USAGoogle Scholar
- Bosq D (2000) Linear processes in function spaces theory and Applications Lecture Notes in Statistics. Springer, New YorkGoogle Scholar
- Cressie NA (1993) Statistics for spatial data. Wiley Series in Probability and Mathematical Statistics, New-YorkGoogle Scholar
- Donoho D (2000) High-dimensional data analysis: the curses and blessings of dimensionality. Lecture delivered at the conference “Math Challenges of the 21st Century” held by the American Math. Society organised in Los Angeles, August 6–11Google Scholar
- Doukhan P (1994) Mixing—properties and examples Lecture Notes in Statistics. Springer, New YorkGoogle Scholar
- Gao S, Collins M (1994) Analysis of grain size trends, for defining sediment transport pathways in marine environments. J Coastal Res 10(1): 70–78Google Scholar
- Györfi L, Härdle, Sarda P, Vieu P (1990) Nonparametric curve estimation from time series. Number 60. Lecture Notes in Statistics, Springer, New-YorkGoogle Scholar
- Li W-V, Shao Q-M (2001) Gaussian processes: inequalities, small ball probabilities and applications. Stochastic processes: theory and methods. Handbook of Statist, page 1861734Google Scholar
- Lu Z (1996) Weak consistency of nonparametric kernel regression under alpha-mixing dependence. Chin Sci Bull 41: 2219–2221Google Scholar