Shrinkage Estimation of Probability Density Functions Based on Spatial Data

Nonparametric estimation of probability density functions, is a very useful tool in statistics. The kernel method is popular and applicable to dependent data, including time series and spatial data. But at least for the joint density, one has had to assume that data are observed at regular time intervals or on a regular grid in space. Though this is not very restrictive in the time series case, it often is in the spatial case. In fact, to a large degree it has precluded applications of nonparametric methods to spatial data because such data often are irregularly positioned over space. In the present article, we develop the well-known Shrinkage estimator of a probability density function for nongridded spatial data. In this respect, we provide the asymptotic characteristics of the proposed estimator under a set of local alternatives.

Nonparametric estimation of probability density functions, is a very useful tool in statistics. The kernel method is popular and applicable to dependent data, including time series and spatial data. But at least for the joint density, one has had to assume that data are observed at regular time intervals or on a regular grid in space. Though this is not very restrictive in the time series case, it often is in the spatial case. In fact, to a large degree it has precluded applications of nonparametric methods to spatial data because such data often are irregularly positioned over space. In the present article, we develop the well-known Shrinkage estimator of a probability density function for nongridded spatial data. In this respect, we provide the asymptotic characteristics of the proposed estimator under a set of local alternatives.