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Breda Munoz Virginia Lesser* Oregon State University

Aquatic Resource Surveys. Designs and Models for. DAMARS. R82-9096-01. A Weighting Class Adjustment Estimator for the Total under a Stratified Sampling Design in a Continuous Domain. Breda Munoz Virginia Lesser* Oregon State University.

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Breda Munoz Virginia Lesser* Oregon State University

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  1. Aquatic Resource Surveys Designs and Models for DAMARS R82-9096-01 A Weighting Class Adjustment Estimator for the Total under a Stratified Sampling Design in a Continuous Domain Breda Munoz Virginia Lesser* Oregon State University

  2. This presentation was supported under STAR Research Assistance Agreement No. CR82-9096-01 awarded by the U.S. Environmental Protection Agency to Oregon State University. It has not been formally reviewed by EPA. The views expressed in this document are solely those of authors and EPA does not endorse any products or commercial services mentioned in this presentation.

  3. Overview • Introduction • Assumptions • Estimator for the Total in a continuous domain • Effect of missing data in estimator for the total • Adjustment estimator

  4. John Day stream network Assumptions • probability sample • Estimate of the population total of a variable Y • Missing at random

  5. Estimating the Total • Horvitz-Thompson Estimator for the total in a continuous domain (Cordy, 1993): - Unbiased • Estimator for the Variance of the total • Other: Total and variance estimators (Yates and Grundy, 1953)Local Variance Estimator (Stevens and Olsen, 2003)

  6. observed missing

  7. HT-total estimator under missing data 70% 89% 92% 15% missing 30% missing 50% missing

  8. missing observed

  9. Accounting for missing data

  10. Variance of the Adjustment Estimator • Observe that:

  11. Variance of the Adjustment Estimator

  12. Variance of the Adjustment Estimator

  13. Population: John Day Middle Fork stream reaches • Area of 785 mi2 • 143 stream reaches divided in survey segments (~1 mile) • 6536 survey segments • We simulate a continuous multivariate normal spatial random process

  14. Population: John Day Middle Fork stream reaches • The population of stream reaches was stratified in 6 strata based on the number of survey segments: “<10 ” “10-20” “20-30” “30-50” “50-100” “>100” • 1,000 samples of size 100

  15. Data

  16. 15% Missing Rate 30% Missing Rate 50% Missing Rate 94.8% 94.1% 77.4%

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