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Spatial statistical models that use flow and stream distance 总被引:6,自引:1,他引:6
Jay M. Ver Hoef Erin Peterson David Theobald 《Environmental and Ecological Statistics》2006,13(4):449-464
We develop spatial statistical models for stream networks that can estimate relationships between a response variable and
other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment.
There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both.
The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance
model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow
and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against
a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and
by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial
models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data
set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that
only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that
uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block
kriging predictions.
Received: July 2005 / Revised: March 2006 相似文献
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Jay M. Ver Hoef 《Environmental and Ecological Statistics》2008,15(1):3-13
Classical sampling methods can be used to estimate the mean of a finite or infinite population. Block kriging also estimates
the mean, but of an infinite population in a continuous spatial domain. In this paper, I consider a finite population version
of block kriging (FPBK) for plot-based sampling. The data are assumed to come from a spatial stochastic process. Minimizing
mean-squared-prediction errors yields best linear unbiased predictions that are a finite population version of block kriging.
FPBK has versions comparable to simple random sampling and stratified sampling, and includes the general linear model. This
method has been tested for several years for moose surveys in Alaska, and an example is given where results are compared to
stratified random sampling. In general, assuming a spatial model gives three main advantages over classical sampling: (1)
FPBK is usually more precise than simple or stratified random sampling, (2) FPBK allows small area estimation, and (3) FPBK
allows nonrandom sampling designs. 相似文献
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