Maximum Likelihood Estimation for Parametric Interval Symbolic Data

• Main Authors: WU,SHIN-CHAN, 吳欣展
• Other Authors: HWANG,YI-TING
• Format: Others
• Language: zh-TW
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/06315386930718200818

碩士 === 國立臺北大學 === 統計學系 === 104 === The amount of global data is accumulated dramatically in the past 20 years. Many new developments in statistical science and information technology have been established. It shows that the era of big data is coming. In order to deal with massive data and integrating data, Diday (2006) proposed the symbolic data analysis, where each symbolic object known as a concept might be a category or a group. Since a symbolic object might contain many observations, variables featuring a symbolic object might not be a simple real number and could be an interval and so forth. Under certain parametric assumptions, Le-Rademacher and Billard (2011) discussed the maximum likelihood estimation for interval symbolic data and histogram symbolic data. However, their parametric assumption assumes that the internal variable follows a specific distribution. Normally, the feature of the underlying population is of interest. Instead, this thesis assumes that the variable of interest for the underlying population follows a specific distribution. The distribution of the variable for the symbolic objects is derived. The estimators of parameters are then obtained by the maximum likelihood estimation. Finally, Monte Carlo simulations are used to evaluate the performance of parameter estimates under various parameter situations.