Predictor sort sampling and confidence bounds on quantiles I: asymptotic theory

Steve P. Verrill; Victoria Herian; David W. Green

Treesearch

Predictor sort sampling and confidence bounds on quantiles I: asymptotic theory

Informally Refereed

Authors:

Steve P. Verrill, Victoria Herian, David W. Green

Year:

2004

Type:

Research Paper

Station:

Forest Products Laboratory

Source:

FPL-RP-623

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Download (PDF 672 KB): https://research.fs.usda.gov/download/treesearch/68679.pdf

Abstract

In this paper we examine the effect of predictor sort sampling on one-sided confidence bounds for normal quantiles. We have found that standard noncentral T theory that ignores the predictor sort nature of the sampling leads to Ȳ − kS bounds that are overly conservative. On the other hand, maximum likelihood methods yield non-conservative bounds even for fairly large sample sizes. We provide an asymptotic result that yields the appropriate corrections for the standard noncentral T approach.

Keywords

concomitants of order statistics, tolerance bounds, asymptotics, allowable strength property

Citation

Verrill, Steve P.; Herian, Victoria L.; Green, David W. 2004. Predictor sort sampling and confidence bounds on quantiles I: asymptotic theory. Research Paper FPL-RP-623. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 67 p.