| Summary: | 碩士 === 國立中正大學 === 數學系統計科學研究所 === 106 === Unlike classical data, interval data consists of a collection of intervals instead of single values. Since its unique structure, statistical theories and methods developed for classical data may not be applied directly.
Thus, in this thesis we focus on studying two aspects of interval data. First, we aim at developing a new approach related to the model fitting for interval data, and compare our proposed method with the existing methods. The presence of outliers might bring seriously adverse effects on the results of model fitting leading to the inaccurate conclusion. Hence, outlier detection is an essential procedures in the process of statictical analysis. This becomes the second focus of this thesis. To this end, we propose a new approach via constructing the likelihood functions of order statistics, where the underlying mean and variance functions are involved with the linear regression model. Then we employ the local influence introduced by Cook (1986) to identify aberrant intervals. Last but not least, simulation studies and real data examples are provided to illustrate our proposed methods.
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