# 臺灣博碩士論文加值系統

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 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 122 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 293 Asymptotic Property of Play-the-winner Strategy under the Markov Chain Scheme 394 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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 1 具隨機性投資標的之風險管理－以台灣公益樂透彩為例 2 預測二元有序數列之普適提方法

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