Saddlepoint Approximations for Statistical Inference of PPP Sample Estimates

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Abstract:

Sampling with probability proportional to predictions (PPP) can be very efficient; yet variance estimators for sample estimates rely on a first-order Taylor series expansion which can be seriously biased for small sample sizes (n ≤10). Forestry application of sampling with PPP often involves volume estimation of a few trees selected with PPP. To improve estimates of sampling variance in these applications this study illustrates how saddlepoint approximations can produce estimates of standard deviations that are closer to benchmark values than current popular variance estimators. Confidence intervals based on the traditional variance estimator and a Student's t-distribution could be improved upon by using the variance efficient sample size minus one as the degree of freedom instead of simply sample size minus one. A bootstrap procedure adapted to PPP sampling produced variable and generally inferior results. For small samples (n <10) estimating the PPP sampling variance via saddlepoints approximations appears worthwhile.

Keywords: BOOTSTRAP; CONFIDENCE; COVERAGE; EQUATIONS; ESTIMATING; ESTIMATION; FOREST; INTERVALS; INVENTORY; PROBABILITY; STUDENT'S; T-DISTRIBUTION; VARIANCE; VOLUME

Document Type: Research Article

DOI: http://dx.doi.org/10.1080/028275801300088288

Affiliations: Natural Resources Canada, Canadian Forest Service, Pacific Forestry Center, 506 West Burnside Rd., Victoria BC V8Z 1M5, Canada

Publication date: March 1, 2001

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