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used estimates the standard error of the mean assuming independent observations. 
As a result, the confidence interval is not capturing the effect of the spatial depend¬ 
encies nor is it based on the fact that we are predicting a value for the unobserved 
site rather than estimating a mean. The development described by Tomczak (1998) 
should be explored further and other alternatives such as block bootstrapping for 
variance estimation as well. 
3.3 NON-PARAMETRIC INTERPOLATION METHODS 
There are many variations on spatial interpolation in addition to kriging and IDW. 
See Cressie (1989) for a review. The committee did not have sufficient time to 
compare all models, but CBP in encouraged to continue this research. One promising 
category of models are for interpolation based on non-parametric methods that do 
not rely on measuring and accounting for spatial autocorrelation. All of the non-para¬ 
metric approaches would be based on the assumption that the autocorrelation 
observed in the data is due to unobserved explanatory variables and hence alterna¬ 
tive modeling approaches are not unreasonable. The particular set we mention are 
the regression type analyses with the locational indices (northings, eastings) used as 
explanatory variables. Examples include generalized additive models (Hastie and 
Tibshirani, 1990), high-order polynomials (Kutner, Nachtsheim, Neter, and Li, 
2004), splines (Wahba, 1990), and locally weighted regression (“loess” or “lowess”, 
Cleveland and Devlin, 1988). In some kriging and IDW methods, large-scale trend 
is modeled relatively smoothly using locational indices and local smaller-scale vari¬ 
ation is modeled using the estimated autocorrelation in conjunction with the values 
of the variable at nearby observed sites. The nonparametric methods replace estima¬ 
tion of the local variation based on correlation functions with models of the 
large-scale trend that are less smooth and more responsive to the spatial variation in 
the observed data. A visual demonstration is given in Figure 3.1 which shows a one¬ 
dimensional dataset with Y as the variable to be predicted and X as the location along 
the one dimensional axis. For example, X could be distance from the mouth of a river 
and Y could be chlorophyll a concentration. 
One advantage of these approaches is that each of the methods has extensive statis¬ 
tical research into estimation of model parameters as well as standard errors for those 
parameters and for predictions at interpolation sites. Another is that the main 
modeling decisions are related to bandwidth selection or degree order of polynomial 
to fit. These decisions can be automated by developing rules for roughness of fit 
based on reduction in MSE as compared to modeling a straight line (in X). Disad¬ 
vantages are the same as for kriging, all model estimation is data dependent which 
means that the spatial configuration and number of sampling sites has a direct influ¬ 
ence on the predictions and their error estimates. In addition, a study done by Laslett 
(1994) comparing kriging and splines indicated that the two methods are similar in 
predictive power but for certain sampling regimes kriging performs better. We 
recommend more study since the non-parametric approaches would be easier to 
implement than kriging. 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
