A Model-Dependent Ratio Estimator of Variance for Two-Stage with Regression Designs

• Activity Number: 293
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Steen Magnussen*+ and Erik Næsset and Terje Gobakken
• Companies: Canadian Forest Service and Norwegian University of Life Sciences and Norwegian University of Life Sciences
• Keywords: sampling design ; ratio-to-size estimator ; forest inventory ; cluster sampling ; large scale survey

Abstract

Design-based estimators for two-stage SRS with regression can suffer from a lack of precision (efficiency) when the primary sampling units (PSU) vary in size and PSU-totals are approximately proportional to the size of a PSU. Precision may deteriorate further for domain-specific estimators when PSUs contain elements from different domains. Model-dependent ratio-to-size estimators are more efficient. This study introduces a new model-dependent variance estimator for a two-stage ratio estimator. The new estimator of variance is derived from a single stage estimator of a variance of a ratio under the assumptions: i) the target variable (y) is approximately equal to the sum of a model-dependent prediction and two error terms capturing lack-of-fit and model-errors, and ii) an unbiased estimate of the true model parameters. Simulations confirmed the negative effects of unequal PSU sizes on the precision of design-based estimators and a superior performance of the proposed estimator of variance. Analysis of a regional two-stage survey of forest biomass corroborated these findings.