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We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods for constructing the standard error and the critical value. The standard error is constructed using population...
Contexts in source publication
Context 1
... is analogous to inference in small-sample Gaussian models using critical values from the Student-t distribution. Figure 5 shows the effect of the uncertainty in σ 2 on the expected length of 95% confidence intervals in the U.S. states spatial correlation designs, by comparing the expected length of the SCPC confidence interval in the i.i.d. model to the the length with σ 2 known: this relative length is E 1 [(cv /1.96)(ˆ σ SCPC /σ)|s], where 1.96 is the standard normal critical value. ...
Context 2
... measurement error of this sort has little effect on the size of SCPC under uniformly distributed locations, but can have a substantial effect for highly concentrated spatial distributions, especially when ρ 0 = 0.02. Figure 5 showed the expected length of the SCPC confidence interval relative to the length of an oracle confidence interval that uses the true value of Var( √ n(y − µ)) conditional on the observed locations s. (As before, in this subsection we keep the conditioning on s and the dependence on n implicit.) For studying efficiency, a more relevant comparison involves the expected length of the SCPC confidence interval relative to a confidence interval that, like SCPC, does not depend on the true (unknown) value of Var( √ n(y − µ)). ...
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