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研究生:蘇靜蓮
研究生(外文):Jing-Lien Su
論文名稱:二元數列之預測方法的模擬比較:預測方法是否需具隨機性?
論文名稱(外文):Simulated Comparison on Some Predictors for Binary Sequences:to Randomize or not to Randomize ?
指導教授:曾玉玲曾玉玲引用關係
指導教授(外文):Yu-Ling Tseng
學位類別:碩士
校院名稱:國立東華大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:56
中文關鍵詞:二元數列預測方法隨機性多數決柏努利大樣本理論馬可夫鏈
外文關鍵詞:binary sequenceplay-the-winnerprediction algorithmMarkov chainrandomizationBernoullipredictorasymptotic property
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  • 被引用被引用:0
  • 點閱點閱:271
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  • 下載下載:43
  • 收藏至我的研究室書目清單書目收藏:0
在這一篇論文之中,我們想要比較不同預測方法在有限樣本時的優劣情形,並且想要知道預測方法中的隨機性是否對於預測二元數列有實質的幫助。透過模擬研究結果發現,對於幾乎所有的二元數列之預測問題而言,任何類型的隨機性對於預測是無益的,因此建議使用多數決方法來預測二元數列。此外,我們亦建構一個在馬可夫鏈模型下多數決方法之大樣本理論。
In this work, we compare the finite sample performances of some prediction algorithms through simulation studies.We also want to see if the randomization is really beneficial in predicting binary sequences.Our study indicates that any sort of randomization is not really favorable for predicting almost all kind of binary data,hence the play-the-winner strategy is suggested.Our study also establishes an asymptotic property of the play-the-winner rule under the Markov chain scheme.
1 Introduction 2
1.1 The Background 2
1.2 Predictors 3
1.3 Motivation 11
1.4 Organization 12

2 Simulated Comparsion of Different Prediction Algorithms 13
2.1 Independent Case 14
2.1.1 Comparisons 14
2.2.2 Summary 15
2.2 Dependent Case 20
2.2.1 Preliminary Results 20
2.2.2 Comparisons 26
2.2.3 Summary 29

3 Asymptotic Property of Play-the-winner Strategy under
the Markov Chain Scheme 39

4 Application and Conclusion 45
4.1 Simple Application to Stock Price Process 45
4.1.1 Data 45
4.1.2 Comparisons 46
4.1.3 Summary 47
4.2 Conclusion 48
[1] Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis, 2nd ed. Springer, Berlin.
[2] Feder, M., Merhav, N. and Gutman, M. (1992). Universal Prediction of individual Sequences. IEEE Trans. Inform. Theory 38 1258-1270.
[3] Gyorfi, L., Lugosi, G. and Morvai, G. (1999). A Simple Randomized Algorithm for Sequential Prediction of Ergodic Time Series. IEEE Trans. Inform. Theory 45(7) 2642-2650.
[4] Haussler, D., Kivinen, J. and Warmuth, M.K. (1998). Sequential Prediction of Individual sequences Under General Loss Function. IEEE Trans. Inform. Theory 44(5) 1906-1925.
[5] Hutter, M. (2001). New Error Bounds for Solomomoff Prediction. J.Comput. Syst. Sci. 62(4) 653-667.
[6] Lerche, H. R. and Sarkar, J. (1994). The Blackwell Prediction Algorithm for Infinite 0-1 Sequence, and a Generalization. Statistical Decision Theory and Related Topics V, Springer, Berlin, 503-511.
[7] Matsuyama, H., Nakamura, Y., Tateno, S., Takeda, K. and Tsuge, Y. (2001). Prediction of Binary Azeotropic Temperatures by use of Topological and Thermodynamic Conditions for Combinations of Azeotropes in Ternary Systems. Kagaku kogaku Ronbun. 27(4) 493-496.
[8] Merhav, N. and Feder, M. (1998). Universal Prediction. IEEE Trans.Inform. Theory 44(6) 2124-2147.
[9] Nastaj, J. and Ambrozek, B. (2001). Binary Adsorption Capacity Prediction of Water and Water Immiscible Organic Compounds on Activated Carbon. Inz. Chem. Procesowa 22(3D) 995-1000.
[10] Ross, S. M. (1997). Introduction to Probability Models, 6th ed. Academic Press.
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