Graduate Thesis Or Dissertation

Estimation of totals for skewed populations in repeated agricultural surveys

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  • The National Agricultural Statistical Service (NASS) conducts quarterly surveys for estimation of some primary commodities produced on farms and ranches. The commodities often have highly skewed distributions with a few farms producing very large amounts. NASS uses dual sampling frames comprised of the list frame for efficient stratification and the area frame for estimation of the part (nonoverlap) of the population that is not included in the list frame. Because the area frame sampling probabilities are relatively small, a few large observations in the nonoverlap sample can greatly influence the usual direct expansion (DE) estimates for population totals. The purpose of this thesis is to investigate modifications of the usual DE estimators which could produce more efficient estimators for the NASS quarterly surveys. An empirical Bayes approach is used as a method for including estimates from previous quarterly surveys to help stabilize the estimate for the current survey. Another approach is to right-censor the very large expanded observations in the nonoverlap sample to produce a censored direct expansion (CDE) estimator. A bias adjustment, formed as the ratio of the DE and CDE sums over the repeated surveys, is applied to the CDE estimator to produce the adjusted censored direct expansion (ACDE) estimator. The empirical Bayes technique is then applied to the ACDE estimates. The empirical Bayes and censored estimates are calculated for total hogs and pigs in the nine quarterly surveys: March 1987-March 1989 from Indiana, Iowa, and Ohio. A bootstrap method is constructed to estimate and compare the biases, standard errors, and root mean square errors (RMSE's) of the various estimators. Only a slight reduction in RMSE resulted from censoring the very large expanded observations in the nonoverlap sample. Application of the empirical Bayes technique to either the DE or the ACDE estimators reduced the average RMSE by about 10% in each of the three states.
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