Each year, the National Agricultural Statistics Service (NASS) publishes an estimate of the number of farms in the United States based on the June Area Survey (JAS). Independent studies showed that the JAS number of farm indications have significant undercount due to misclassification. To adjust for this undercount, a follow-on survey to the JAS called the Annual Land Utilization Survey (ALUS) has been proposed. ALUS is designed and developed based on the Farm Numbers Research Project (FNRP). NASS conducted the FNRP in the fall of 2009 (Abreu, McCarthy and Colburn, 2010). ALUS samples from all JAS segments containing any estimated or non-agricultural JAS tracts. For a selected segment, all estimated and non-agricultural JAS tracts will be re-evaluated. The collection of eligible segments in a particular year will be called the ALUS population. The sample allocation of ALUS segments to each state-stratum combination considers two factors: the proportion of the ALUS population in the stratum and the proportion of the FNRP adjustment from non-agricultural tracts in the stratum. ALUS can be treated as a second phase to the JAS. The two-phase stratified design, JAS-ALUS, can be applied to any estimate produced by the JAS. However, ALUS has non-response. In this paper, methodology for a three-phase sampling design is developed by extending the two-phase sampling design methodology proposed by Sarndal and Swensson (1987). A general sampling design is allowed in each phase; that is, the inclusion probabilities in each phase are arbitrary. The estimator is unbiased, and an unbiased estimator for the variance is provided. Here, this method is applied to the two-phase JAS-ALUS with the third phase being response/non-response.


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