| Summary: | 碩士 === 國立中央大學 === 統計研究所 === 105 === In classic statistical theory, accuracy assessments of estimators are usually made without taking model selection into account. However, Selection-based estimates change values discontinuously at the boundaries of model regimes. Bootstrap smoothing, which is provided by Efron (2014), is a technique can smooth such these “jumpy” estimates. In this thesis, we apply this method in Hidden Markov Models (HMM) to construct a better confidence interval under model uncertainty. Moreover, we reduce the computation burden in bootstrap framework assisted by Gaussian mixture models, which can be considered a special case of HMMs. An empirical study is applied on the stock market.
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