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A Comparison Of Estimators For The Mean Of A Finite Population, Based On A Systematic Sample

Larry L. Huff, Diem-Tran Kratzke, Gordon Mikkelson, and Sandra A. West


In this paper we empirically compare several mean estimators for a finite population based on a systematic sample. This research began with a quality improvement project for two Bureau of Labor Statistics' establishment programs that collect monthly employment data: the Quarterly Census of Employment and Wages (ES-202) program and the Current Employment Statistics (CES) survey. The ES-202 program is compiled using data from quarterly reports of business establishments that are covered under the Unemployment Insurance laws in the United States. The CES survey collects monthly employment from a voluntary sample of business firms and uses the ES-202 universe employment data to annually adjust its industry employment totals. A Response Analysis Survey (RAS) was conducted in order to determine the comparability and accuracy of employment data reported to these two programs. Each sample unit was asked several questions pertaining to their response practices for both of these programs. The samples were selected from among the CES reporters of ten participating states. The sample consisted of four panels that were selected approximately three months apart. The panel samples were selected with probability proportional to a measure of size based on size of firm and percent difference between reported employment to the CES and ES-202 programs. Various characteristics of the population are estimated based on their responses to four specific RAS questions. Alternative mean estimators and their estimated standard errors are compared in order to determine the most appropriate estimation techniques. We compare the estimators that treat all four panels separately, as well as estimators that combine the four panels. The general sampling design issues are discussed in Section 2. Background information about the RAS, including a description of the population and sample design, is given in Section 3. The estimation techniques and specific estimators tested are presented in Section 4. Section 5 provides the empirical results. The conclusions of the study are summarized in Section 6.