On certain alternative mean square error estimators in complex survey sampling |
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| Institution: | 1. University of South Carolina, Columbia, SC 29208, USA;2. Wharton Financial Institutions Center, Philadelphia, PA 19104, USA;3. European Banking Center, Tilburg, The Netherlands;4. DePaul University, Chicago, IL 60604, USA;5. Texas A&M University, College Station, TX 77843, USA;6. Washington University in St. Louis, St. Louis, MO 63130, USA;1. Graduate School of International Studies, Yonsei University, Seoul, Republic of Korea;2. School of Management, Royal Holloway, University of London, Egham, UK;3. Department of e-Business, Dongyang Mirae University, Seoul, Republic of Korea;1. Infection Prevention & Control, Environmental Services, & Microbiology Laboratory, St. Joseph Mercy Oakland, Pontiac, MI;2. Xenex Disinfection Services, San Antonio, TX;3. Department of Infection Prevention Management, Integrated Clinical Services, Trinity Health, Livonia, MI |
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| Abstract: | Rao (J. Indian Statist. Assoc. 17 (1979) 125) has given a ‘necessary form’ for an unbiased mean square error (MSE) estimator to be ‘uniformly non-negative’. The MSE is of a homogeneous linear estimator ‘subject to a specified constraint’, for a survey population total of a real variable of interest. We present a corresponding theorem when the ‘constraint’ is relaxed. Certain results are added presenting formulae for estimators of MSEs when the variate-values for the sampled individuals are not ascertainable. Though not ascertainable, they are supposed to be suitably estimated either by (1) randomized response techniques covering sensitive issues or by (2) further sampling in ‘subsequent’ stages in specific ways when the initial sampling units are composed of a number of sub-units. Using live numerical data, practical uses of the proposed alternative MSE estimators are demonstrated. |
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