On the Adaptive Estimation of A Distribution Function

• Main Authors: Chang, Chin-Ni, 張瑾怩
• Other Authors: Cheng Wei-hou
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/45459491459241122093

碩士 === 國立東華大學 === 應用數學研究所 === 84 === To estimate an unknown distribution function F(x), the empirical distribution function Fn(x) is a very popular choice. If we are dealing with acontinuous and symmetric distribution, then Schuster (1975) proposed anestimator Gn^(x) which shows good performance, but the performance depends a great deal on the estimator of the unknown center of symmetry. But if theunderlying distribution is skewed, Gn^(x) is not appropriate. We would like to propose a good estimator for F(x) when we have littleinformation about the population where our data come from. 'Adaptive' idea wasused which first classifies the data as being symmetric or asymmetric and in the symmetric case as light, medium or heavy tailed and then Gn^(x) with appropriate estimator of center or Fn(x) is used to estimate F(x). Monte Carlostudies were carried out which showed that our estimator is worth recommending.