## Projected Variance for the Model-Based Classical Ratio Estimator II: Sample Size Requirements

### by James R. Knaub, Jr.

**Abstract:**
Here we explore planning for the allocation of resources for use in obtaining official statistics through model-based estimation. Concentration is on the model-based variance for the classical ratio estimator (CRE). This has application to quasi-cutoff sampling (simply cutoff sampling when there is only one attribute), balanced sampling, econometrics applications, and perhaps others. Multiple regression for a given attribute can occasionally be important, but is only considered briefly here. Nonsampling error always has an impact. Allocation of resources to given strata should be considered as well. Here, however, we explore the projected variance for a given attribute in a given stratum, to judge the relative impact of factors needed for planning, at that base level. Typically one may consider the volume coverage for an attribute of interest, or related data, say regressor data, to be important, but standard errors for estimated totals are needed to judge the adequacy of a sample. Thus the focus here is on a ‘formula’ for estimating sampling requirements for a model-based CRE, analogous to estimating the number of observations needed for simple random sampling. An example is used to apply this to cutoff sampling, quasi-cutoff sampling, and balanced sampling.
**Key Words: **
Classical Ratio Estimator, Coverage, Measure of Size, Model-Based Estimation, Official Statistics, Resource Allocation Planning, Weighted Least Squares Regression

**Author:**

James R. Knaub, Jr., knaub1977@comcast.net

**Editor:**
Richard G. Graf,rgraf@sunstroke.sdsu.edu

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**NOTE: **This article was revised on November 29, 2013.

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