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Variance Reduction for Radial Line Sampling Coverage Estimators

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Abstract:

It may be convenient to use radial line sampling for coverage estimates in small irregularly shaped areas. Radial line samples emanate from a fixed point located in the interior of the area and would be run according to a randomly selected azimuth. Thus, radial line sampling is analogous to techniques of local stereology, which considers quantitative aspects of spatial structures in the neighborhood of a central point. Coverage estimates from radial line sampling can be based on coverage observed on several sample lines. Several variance reduction techniques commonly used in Monte Carlo integration are proposed to reduce the variance of coverage estimates based on radial line sampling: importance sampling, control variates, and antithetic variates. The success of these techniques in irregularly shaped areas depends on the assumption that total line length is correlated with length of coverage. Radial line sampling as proposed here differs somewhat from ordinary line sampling because coverage estimates are based on squared line lengths.

Keywords: Monte Carlo integration; control variate; importance sampling; stereology; vegetation sampling

Document Type: Research Article

Publication date: April 1, 2008

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