Use of an Antithetic Variate for Better Location of Upper-Stem Height Measurements with Critical Height and Importance Sampling in Horizontal Line Sampling
When critical height importance sampling is used to estimate the volumes of individual trees sampled in horizontal line sampling, upper-stem diameter and height measurements are typically made at randomly chosen locations, which may be difficult to view if they are high on stems located close to the sample line. For more convenient viewing from the sample line, it would be more desirable if upper-stem sample locations were located low on the stem for trees close to the sample line and high on the stem for trees farther away from the sample line, which can be achieved by making random upper-stem sample location a function of the perpendicular distance from the sample line to the sample tree. To do this, a uniform random variate is formed by using the ratio of stem diameter at critical height to basal diameter, where the critical height is the well-known height at which the upper-stem appears to be “borderline” when a point sampling angle gauge is used. The antithetic variate is then formed by subtraction from unity. This antithetic variate will be used to obtain a sample height from an importance sampling distribution. An unbiased estimate of individual tree volume is then obtained by using importance sampling. When the importance sampling volume estimates are used in the horizontal line sampling total volume estimator, an unbiased estimate of total volume is obtained, which is free from volume table bias. A critical height sampling estimator adapted to horizontal line sampling is also presented.
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