Fisher information in censored samples from folded and unfolded populations

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• 作者：Lira Pi ; H. N. Nagaraja
• 关键词：Order statistics ; Fisher information ; Type II censoring ; Folded distribution ; Unfolded distribution ; Laplace distribution ; Exponential distribution
• 刊名：Metrika
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：78
• 期：7
• 页码：785-806
• 全文大小：527 KB
• 参考文献：Arnold BC, Balakrishnan N, Nagaraja HN (2008) A first course in order statistics. SIAM, PhiladelphiaMATH View Article
  Balakrishnan N, Govindarajulu Z, Balasubramanian K (1993) Relationships between moments of two related sets of order statistics and some extensions. Ann Inst Stat Math 45(2):243鈥?47MATH MathSciNet View Article
  David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, HobokenMATH View Article
  Govindarajulu Z (1963) Relationships among moments of order statistics in samples from two related populations. Technometrics 5(4):514鈥?18MATH MathSciNet View Article
  Park S (1996) Fisher information in order statistics. J Am Stat Assoc 91(433):385鈥?90MATH View Article
  Zheng G, Gastwirth JL (2000) Where is the Fisher information in an ordered sample? Stat Sin 10:1267鈥?280MATH MathSciNet
  
• 作者单位：Lira Pi (1)
  H. N. Nagaraja (2)
  
  1. Department of Statistics, The Ohio State University, Columbus, OH, 43210, USA
  2. Division of Biostatistics, College of Public Health, The Ohio State University, Columbus, OH, 43210, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1435-926X

文摘

Fisher information (FI) forms the backbone for many parametric inferential procedures and provides a useful metric for the design of experiments. The purpose of this paper is to suggest an easy way to compute the FI in censored samples from an unfolded symmetric distribution and its folded version with minimal computation that involves only the expectations of functions of order statistics from the folded distribution. In particular we obtain expressions for the FI in a single order statistic and in Type-II censored samples from an unfolded distribution and the associated folded distribution. We illustrate our results by computing the FI on the scale parameter in censored samples from a Laplace (double exponential) distribution in terms of the expectations of special functions of order statistics from exponential samples. We discuss the limiting forms and illustrate applications of our results.