Sample quantiles and additive statistics: Information,sufficiency, estimation |
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| Institution: | 1. The Laboratory of Physiological Hygiene and Exercise Science, University of Minnesota Twin Cities, Minneapolis, MN 55455, USA;2. Department of Orthopedic Surgery, Mayo Clinic, Rochester, MN 55905, USA;3. Department of Physical Education, Inha University, Incheon 22212, Republic of Korea;4. Department of Kinesiology, Health and Nutrition, University of Texas at San Antonio, San Antonio, TX 78249, USA |
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| Abstract: | The order of the increase in the Fisher information measure contained in a finite number k of additive statistics or sample quantiles, constructed from a sample of size n, as n → ∞, is investigated. It is shown that the Fisher information in additive statistics increases asymptotically in a manner linear with respect to n, if 2 + δ moments of additive statistics exist for some δ > 0. If this condition does not hold, the order of increase in this information is non-linear and the information may even decrease. The problem of asymptotic sufficiency of sample quantiles is investigated and some linear analogues of maximum likelihood equations are constructed. |
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