Estimation and Accuracy After Model Selection in Hidden Markov Models

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賴志嘉(Jhih-Jia Lai) 查詢紙本館藏

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統計研究所

論文名稱

(Estimation and Accuracy After Model Selection in Hidden Markov Models)

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摘要(中)

在古典的統計理論當中，統計量的精準評估通常並不把模型選取納入考量。然而，若是先以資料為基準選取適合的模型，並以此模型計算出我們有興趣的統計估計量;這個估計量的值將在模型與模型的邊界形成不連續的斷面。換句話說，考慮模型選取的統計估計量，會因選取不同模型而有著不連續的跳動。為了解決此一問題，Efron在2014年提出了平滑拔靴法，透過模型平均的方式將此不連續的跳動平滑化來提升統計量的精準度。本研究將以此方法為基礎，在考慮模型不確定的狀況下對隱馬可夫模型進行統計量的精準評估。更進一步的，為了節省拔靴法下隱馬可模型的大量計算，在研究中借助高斯混和模型更快的完成拔靴法。實際上，高斯混和模型可以視為隱馬可夫模型的一個特殊例子。最後，給出股票市場的實例分析。

摘要(英)

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.

關鍵字(中)

★ 裝袋算法
★ 平滑拔靴法
★ 隱馬可夫模型
★ 赤池信息量準則
★ 模型平均

關鍵字(英)

★ Bagging
★ Bootstrap smoothing
★ Hidden Markov models
★ AIC
★ Model averaging

論文目次

摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . ii
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . .iv
1 Introduction . . . . . . . . . . . . . . . . . . . . . .1
1.1 Background . . . . . . . . . . . . . . . . . . . . . .1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . .2
2 Hidden Markov Models . . . . . . . . . . . . . . . . . .4
2.1 The Basic . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Forward and Backward Probability . . . . . . . . . . .6
3 Methodology . . . . . . . . . . . .. . . . . . . . . . .7
3.1 Parameter Estimation . . . . . . . . . . . . . . . . .7
3.2 The Bootstrap Methods . . . . . . . . . . . . . . . .10
3.2.1 Naive Bootstrap with normal approximation . . . . .10
3.2.2 Bootstrap Smoothing with normal approximation . . .11
3.2.3 Bias-Correction and Acceleration . . . . . . . . .12
4 Simulation Study . . . . . . . . . . . . . . . . . . . 13
4.1 2-state HMM . . . . . . . . . . . . . . . . . . . . 15
4.2 3-state HMM . . . . . . . . . . . . . . . . . . . . 17
4.3 Efficient Computation method . . . . . . . . . . . .20
5 Empirical Study . . . . . . . . . . . . . . . . . . . .23
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . 26
References . . . . . . . . . . . . . . . . . . . . . . . 28
A Appendix . . . . . . . . . . . . . . . . . . . . . . . 30

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指導教授

傅承德(Cheng-Der Fuh)

審核日期

2017-7-6

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