Nonparametric Estimation of the Probability Density Functions for Irregularly Observed Spatial Data

• Activity Number: 303
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Zudi Lu*+
• Companies: University of Adelaide
• Keywords: random field ; irregularly positioned spatial data ; marginal and joint density functions ; nonparametric method ; mixed expanding and infill domain asymptotics ; asymptotic normality and consistency

Abstract

Nonparametric estimation methods are well established for time series, but are far less used for spatial random variables. Perhaps the most important reason has been the fact that the sampling points are often irregularly positioned in space. The spatial analysis has been almost completely dominated by linear parametric models; e.g. parametric models for covariance functions (or variogram) in kriging (Cressie 1993, Stein 1999) although there are some exceptions. The nonparametric theory has so far almost exclusively been developed for the regular grid case (Tran 1990, Hallin et al 2001, 2004, Gao et al 2006, Lu et al 2007), which does not quite have the potential applications that one would wish for.

The purpose of this paper is to try to break out of this confinement. We make an attempt to construct an asymptotic theory for nonparametric density estimation, both marginal and joint, for a random field with irregularly placed observations, under a mixed expanding and infill domain approach. This represents our first step in this direction, jointed with Dag Tjostheim.