跳到主要內容

簡易檢索 / 詳目顯示

回結果列表
研究生： 林鼎鈞
Ding-Jyun Lin
論文名稱： 隨機樣本數信賴區間程序的評估與比較
Evaluation and Comparison for Random-Sample-Size Confidence Interval Procedures
指導教授： 葉英傑
Ying-chieh Yeh
口試委員:
學位類別： 碩士
Master
系所名稱： 管理學院 - 工業管理研究所
Graduate Institute of Industrial Management
論文出版年： 2020
畢業學年度： 108
語文別： 中文
論文頁數： 51
中文關鍵詞： 隨機模擬 、區間估計
相關次數： 點閱：9  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 本篇使用了信賴區間評估準則來評估兩個近期推出的隨機樣本數之信賴區間程序。從使用電腦模擬開始，學者將統計方法應用在模擬出的結果。也因為如此，學者紛紛開始研究新的統計方法，從一開始的固定樣本數信賴區間程序到後來的隨機樣本數信賴區間程序。而有了這麼多的方法，也需要一套標準來評估他們的優劣。傳統的評估標準由許多面向來評估一個信賴區間程序的好壞，但多面向也帶來了不少缺點，像是各面向之間互相矛盾，這也讓信賴區間程序的發展受到了影響，因為無法設計出同時滿足各面向評估標準的信賴區間程序。後來 Yeh 和 Schmeiser 提出了單一準則的評估方法 VAMP1RE，讓評估信賴區間程序較為簡單，一開始 VAMP1RE 僅能使用在固定樣本數之信賴區間程序，後來隨著新的信賴區間程序發展，套用了序列停止條件，修改為隨機樣本數也可以使用的一般化 VAMP1RE。有了一般化的 VAMP1RE 之後，即可對近期的 ASAP3 以及 Skart 兩個信賴區間程序做評估比較。
    本篇將先介紹信賴區間程序，從基本的 t 分配信賴區間到近期的 ASAP3 與 Skart，了解信賴區間程序是如何發展之後接著介紹信賴區間評估標準，從過去多面向的評估標準到後來單一準則的 VAMP1RE 以及一般化 VAMP1RE 最後使用一般化 VAMP1RE 來評估 ASAP3 與 Skart。藉由評估的結果判斷後期推出的信賴區間程序是否真的比其前面的信賴區間又更加準確。同時也藉由傳統評估方法與 VAMP1RE 比較，了解新的評估準則在評估結果是否會更方便判斷，提高判斷的效率。

    This paper uses the confidence interval procedure criteria to evaluate and compare the two recently introduced random sample size confidence interval procedures. Beginning with the use of computer simulations, scholars apply statistical methods to the simulated results. Because of this, scholars have begun to study new statistical methods. From the beginning of the fixed sample size confidence interval procedure to the random sample size confidence interval procedure. With so many methods, a set of criteria is needed to assess their quality. The traditional criteria are used to evaluate the quality of a confidence interval procedure by many aspects, but many aspects also bring a lot of shortcomings, such as the contradictions between the various aspects. Later, Yeh and Schmeiser proposed a single criterion, VAMP1RE. At the beginning, VAMP1RE can only use the confidence interval procedure in the fixed sample size. With the development of the new confidence interval procedure, the sequential stopping rule is applied and the generalized VAMP1RE can be used to evaluate the random sample size confidence interval procedure. With the generalized VAMP1RE, we can evaluate the recent ASAP3 and Skart two confidence interval procedures.
    This paper will first introduce the confidence interval procedure, from the basic t- distribution interval to the recent ASAP3 and Skart. Understand how the confidence interval procedure develops and then introduce the confidence interval criterion. Finally, the generalized VAMP1RE was used to evaluate ASAP3 and Skart. It is judged by the result of the evaluation whether the later-suggested confidence interval program is actually more accurate than its previous confidence interval.

    中文摘要 ....................................................................... i Abstract ....................................................................... ii 圖目錄 .......................................................................... iv 表目錄 ............................................................................v 一、緒論 .........................................................................1 1-1 研究背景 ...................................................................1 1-2 研究動機 ...................................................................1 1-3 研究結構 ...................................................................2 二、文獻探討 ..................................................................4 2-1 信賴區間程序(Confidence Interval Procedure) .........4 2-1-1 固定樣本數之信賴區間程序......................................7 2-1-2 隨機樣本數之信賴區間程序......................................7 2-2 CIP 評估準則(CIP Criterion) .....................................12 2-2-1 傳統評估準則.........................................................12 2-2-2 VAMP1RE.............................................................14 三、研究方法 ..................................................................18 3-1 實驗方法與參數定義 ..................................................18 3-2 實驗步驟 ..................................................................18 四、實驗數據 ..................................................................21 4-1 AR(1)樣本之評估結果.................................................23 4-2 M/M/1 樣本之評估結果..............................................27 五、結論 ........................................................................35 5-1 結論 ........................................................................35 5-2 未來展望 .................................................................35 參考文獻 ........................................................................36 附錄 ..............................................................................38

    1.Alexopoulos C. and Goldsman, D.M. (2004) To batch or not to batch. ACM Transactions on Modeling and Computer Simulation, 14, 76-114
    2. Alexopoulos, C. & Kelton, W. D. (2017) A Concise History Of Simulation Output Analysis, Proceedings of the 2017 Winter Simulation Conference, 115- 130
    3. Kang, K. and Schmeiser, B. (1990) Graphical methods for evaluating and comparing confidence-interval procedures. Operations Research, 38(3), 546–553
    4. Kim, S. & Nelson, B. L. (2007) Recent Advances In Ranking And Selection,
    Proceedings of the 2007 Winter Simulation Conference, 162-172
    5. Law, A. M. & Kelton, W.D. (1984) Confidence Intervals for Steady-State Simulations: I. A Survey of Fixed Sample Size Procedures, Operations Research, Vol. 32, No. 6 (Nov. - Dec., 1984), pp. 1221-1239
    6. Lada, E. K. & Wilson, J. R. (2006) A wavelet-based spectral procedure for steady-state, simulation analysis European Journal of Operational Research 174, 1769–1801
    7. Royston, J. P. (1981) Algorithm AS 181: The W Test for Normality, Journal of the Royal Statistical Society. Series C (Applied Statistics), 176-180
    8. Royston, J. P. (1982) Algorithm AS 177: Expected Normal Order Statistics (Exact and Approximate), Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 31, No. 2, pp. 161-165
    9. Royston, P. (1995) Remark AS R94: A Remark on Algorithm AS 181: The W- test for Normality, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 44, No. 4, pp. 547-551
    36
    10. Schmeiser, B. (1982) Batch Size Effects in the Analysis of Simulation Output, Operations Research, Vol. 30, No. 3, pp. 556-568
    11. Schmeiser, B., Song, W. T. (1989) Inverse-Transformation Algorithms For Some Common Stochastic Processes, Proceedings of the 1989 Winter Simulation Conference,490-496
    12. Sargent, R. G., Kang, K. & Goldsman, D. (1992) An Investigation of Finite- Sample Behavior of Confidence Interval Estimators, Operations Research, Vol. 40, No. 5 (Sep. - Oct., 1992), pp. 898-913
    13. Steiger, N. M. & Wilson, J. R. (2002) An Improved Batch Means Procedure for Simulation Output Analysis, Management Science, Vol. 48, No. 12 (Dec., 2002), pp. 1569-1586
    14. Steiger, N. M., Lada, E. K., Wilson, J. R., Joines, J. A., Alexopoulos, C. & Goldsman, D. (2005) ASAP3: a batch means procedure for steady-state simulation analysis, ACM Transactions on Modeling and Computer Simulation, January 2005, 39-73
    15. Singham, D. I. & Schruben, L. W. (2009) analysis of sequential stopping rules,
    Proceedings of the 2009 Winter Simulation Conference, 723-730
    16. Song, W. T., Chih, M. & Chuang, S. (2013) Variance Reduction Techniques on Generating M/M/1 Processes in Simulation Output Analysis, IEEE Transactions On Automatic Control, Vol. 58, No. 4, 1035-1040
    17. Tafazzoli, A. & Wilson, J. R. (2010) Skart: A skewness- and autoregression- adjusted batch-means procedure for simulation analysis, IIE Transactions, 43:2, 110-128
    37

    18. Wichura, M. J. (1988) Algorithm AS 241: The Percentage Points of the Normal Distribution, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 37, No. 3, pp. 477-484
    19. Yeh, Y. & Schmeiser, B. W. (2015) VAMP1RE: a single criterion for rating and ranking confidence-interval procedures, IIE Transactions, 47:11, 1203-1216
    20. Yeh, Y. & Schmeiser, B. W. (2018) VAMP1RE: A Generalization to Stochastic Stopping Rules, Technical report

    QR CODE
    :::