Simultaneous estimation of coefficients of variation |
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| Affiliation: | 1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, China;2. Department of Statistics, Kansas State University, Manhattan, KS, United States;1. Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China;2. School of Science, Beijing Jiaotong University, Beijing 100044, China;1. IPAG Business School, 184 Boulevard Saint-Germain, 75006 Paris, France;2. Department of Economics, European University Institute (EUI), Via della Piazzuola; 43, I-50133, Florence, Italy;3. Department of Acc. & Finance, Athens University of Economics & Business (AUEB), 76 Patission str., GR104 34, Athens, Greece;4. Department of Economics, University of Pretoria, Pretoria, 0002, South Africa |
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| Abstract: | An improved asymptotic estimation theory for the coefficient of variation γ is developed under the homogeneity hypothesis that several coefficients of variation are the same. Assuming that homogeneity holds, it is advantageous to combine the data to estimate the common coefficient of variation. However, the combined estimator becomes inconsistent when the equality of the hypothesis does not hold. In this situation, estimators based on pretest and (James and Stein, 1961. Estimation with quadratic loss. Proceeding of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, pp. 361–379) principles are proposed. Asymptotic properties of the shrinkage estimator, positive-part and pretest estimators are discussed and compared with the standard and combined estimators. It is demonstrated that the positive part estimator utilizes the sample and nonsample information in a superior way relative to the ordinary shrinkage estimator. |
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