Publication Details

An evaluation of the properties of the variance estimator used by FIA

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Year Published

2012

Publication

In: McWilliams, Will; Roesch, Francis A. eds. 2012. Monitoring Across Borders: 2010 Joint Meeting of the Forest Inventory and Analysis (FIA) Symposium and the Southern Mensurationists. e-Gen. Tech. Rep. SRS-157. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 53-58.

Abstract

The Forest Inventory and Analysis (FIA) program of the U.S. Forest Service currently conducts inventories utilizing the protocols of the national enhanced FIA Program. Due to the permanent locations of the sample plots, the stratification of the population occurs after the selection of sample units, i.e., post-stratification. In situations where the population is of limited areal extent, this may result in small within-stratum sample sizes. The survey literature provides some guidance on post-stratified sample sizes, but does not specifically address the behavior of estimators when sample sizes are smaller than recommended. It is important for FIA to evaluate how estimators perform across a range of sample sizes, such that samples of sufficient size can be constructed to ensure accurate estimates. The variance estimator used by FIA accounts for a secondary source of variation (V2) due to random within-strata sample sizes that is introduced beyond that obtained from standard proportional allocation of samples to a stratified sample (V1). Thus, each estimate’s variance is composed of two parts. This study utilizes a Monte Carlo simulation to examine the relative contributions of V1 and V2 to the total variance (VTotal) of the estimate. FIA plots from Pennsylvania were treated as a population from which samples of size n are repeatedly drawn and V1, V2, and VTotal calculated for forest area and cubic volume estimates. The sample size varied from 25 to 200 plots. With increasing sample size n, the V1 variance stabilized at sample sizes greater than 60 plots, whereas the V2 variance required sample sizes greater than 125. The ratio of the two variance components (VRAT=V1/V2) was found to increase with increasing n, ranging from 6 to 32 plots for the area estimates and from 8 to 45 plots for the volume estimates.

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Citation

Brown, John P.; Westfall, James A. 2012. An evaluation of the properties of the variance estimator used by FIA. In: McWilliams, Will; Roesch, Francis A. eds. 2012. Monitoring Across Borders: 2010 Joint Meeting of the Forest Inventory and Analysis (FIA) Symposium and the Southern Mensurationists. e-Gen. Tech. Rep. SRS-157. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 53-58.

Last updated on: August 16, 2013