Inference for Spatial Processes Using Subsampling: a Simulation Study

Abstract

Many environmental studies involve the measurement of ecological indices that yield spatially dependent data. One quantity that captures the empirical distribution of ecological measurements is the spatial cumulative distribution function (SCDF). Methods for making inferential statements about SCDFs have only recently been developed, one being that of spatial subsampling. While spatial subsampling produces inferential quantities with known asymptotic properties, the performance of this methodology in a ®nitesample setting has not previously been investigated. In this article, we review the subsampling method and its theoretical justi®cation, and investigate the performance of this method for ®nite samples with a simulation study involving several subsampling designs and types of spatial dependence. The subsampling methodology appears to give quite good results over a range of realistic spatial processes. For application to a set of spatially dependent data, an appropriate subsampling procedure may be designed on the basis of quantities contained in the (estimated) variogram. #

Location‐Specific Cumulative Distribution Function (LSCDF): An Alternative to Spatial Correlation Analysis

“…Since then, Majure et al (1996) formally developed the con-cept and provided the estimation method for SCDF. More recently, the estimation and inference aspects of SCDF were further investigated (for example, Kaiser et al 1997;Lahiri et al 1999).…”

“…A related issue is to determine the significance of the D, statistic. Similar to some newer spatial analpcal techniques, such as SCDF (Overton 1989;Majure et al 1996), of which the properties and inferential power are still under investigation (Kaiser et al 1997;Lahiri et al 1999), the statistical property of LSCDF is currently not known yet. It cannot be determined at this point if it is possible to derive the statistical properties of LSCDF by analpcal methods.…”

Resampling configurations of points through coding schemes

“…They are typically based on depedent (overlapping or non-overlapping) blocks and windows, and may be adapted to the present setting by transformation (10). See Hall (1985), Carlstein (1986), Kiinsch (1989), Possolo (1991), Guyon and Kiinsch (1992), Politis and Romano (1993;1994), Sherman and Carlstein (1994), Brown (1995), Biihlmann and Kiinsch (1995), Hall et al (1995), Cowling et al (1996), Garcia-Soidan and Hall (1997), Kaiser et al (1997), Lahiri et al (1999) and Politis et al (1999), Chapter 5. All these resampling methods work well, if the underlying random field exhibits a short-range dependence (cf.…”

Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method

“…, K and hence, can be easily found by arranging the ξ * i n p 's in an increasing order. Finite sample performance of the method and the choice of the subsampling parameters can be found in Kaiser, Hsu, Cressie, and Lahiri (1997). Also, for an application of the subsampling method to a real data set and for overlapping versions of the subsampling method, see Lahiri, Kaiser, Cressie, and Hsu (1999).…”