## Projected Variance for the Model-Based Classical Ratio Estimator

### 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, which has use in quasi-cutoff sampling, balanced sampling, and in econometrics applications. Other applications for this article in other areas of statistics may arise. Multiple regression for a given attribute can be important, but is only considered briefly here. The need for data to estimate for multiple attributes is also important, and must be considered. 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 see the relative impact of factors needed for planning, for each such case. Typically one may consider the volume coverage for an attribute of interest, or related data, say regressor data, to be important, but relative standard errors for estimated totals, or confidence bounds, are needed, to have a better idea of the adequacy of a sample.
**Key Words: **
Coverage, econometrics, establishment surveys, measure of size, model-based estimation, official statistics, quasi-cutoff sampling, regression through the origin, resource allocation planning, sample surveys, total survey error, 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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**(There is an ADENDDUM to this article submitted 12/10/13):** You can read the article in
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**(There is a second ADENDDUM to this article submitted 5/23/13):** You can read the article in
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