- 學位論文
控制變數與Balanced Bootstrap 在系統模擬之應用與分析
The Incoporation of Balanced Bootstrap into Control Variates in Simulation Experiment
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摘要
變異數縮減技術是一種於模擬樣本間注入相關性或於模擬實驗中擷取額外 的資訊以降低估計值變異數的技巧。在一般變異數縮減技術中，控制變數 技巧的優點在於任何模擬實驗皆適用而廣為系統模擬者所採用。若想對估 計式的變異數做進一步了解的話;往得重複模擬多次，需要龐大的計算成 本，而利用Bootstrap的重抽樣方法法則是簡易又不耗費額外的成本。傳 統的Bootstrap是將樣本數值視為經驗機率分配的根本,從其中重覆抽樣， 以取得更多的樣本數。但是得到的估計式為經驗機率分配中對應的參數的 一個偏估計式 (Biased Estimator)。而而Davision,Hinkley, Schechtman(1986)所提出的Balanced Bootsrtap方法則改進傳統的 Bootstrap 抽樣方法，使我們所得到的估計式為一個不偏估計式( Unbiased Estimator)。如此能提高估計式的精確度。本研究著重於將控 制變數技巧注入模擬之系統中， 得到一組資料，從而用 Balanced Bootstrap重抽樣方法產生多組相關資料。根據樣本資料分分析樣本模擬 方法將此法應用於隨機系統之中，以驗証其適用性。同時亦;比較兩種不 同的抽樣方法對隨機系統之影響。
並列摘要
Variance reduction techniques(VRTs)are experimential design and analysis techniquesysed to increase the precision if sampl- ing- based point estimators without a corresponding increasing in sampling efforts.We consider control variates(CV) which is one of VRTs.Using CV is feasible in any stochastic simulation,and applying CV to eatimate one paramenter does not confilt with estimating other paramenter. The bootsrap is an tool for estimating the accuracy of an unknown paramenter. The ordinary bootstrap resamples are genera ted by simple random sampling with replacement from the ordinary sampling which called uniform bootstrap.A balanced bootsrap res- amples are generated by duplicating each observation in the ori- dinal sample same times so that the resampling variation can be reduced and a significant improvement is that we can get an unbiased estimator. In this thesis,we incorporate balanced bootsrap into control to variates in a simulation experiment.The result will be appl- ied M/M/1 and M/G/1 queueing systems.We also compare the rela- tive effects between from the precision and sample sizes view- points ordinary bootstrap and balanced bootsrap.