國立高雄大學圖資館 |

Language: English

Back

估計隨機向量函數條件尾部期望值之重點抽樣法 = An Importanc...

國立高雄大學統計學研究所碩士班

估計隨機向量函數條件尾部期望值之重點抽樣法 = An Importance Sampling of Conditional Tail Expectations for Functions of Random Variables

Record Type:	Language materials, printed : monographic
Paralel Title:	An Importance Sampling of Conditional Tail Expectations for Functions of Random Variables
Author:	林家嬅,
Secondary Intellectual Responsibility:	國立高雄大學
Place of Publication:	高雄市
Published:	國立高雄大學;
Year of Publication:	2015[民104]
Description:	29葉圖 : 30公分;
Subject:	條件尾部期望值
Subject:	conditional tail expectation
Online resource:	https://hdl.handle.net/11296/gs9a52
Notes:	107年11月1日公開
Notes:	參考書目：葉29
Summary:	計算一隨機向量之函數的條件尾部期望值與尾部機率在應用領域上都扮演重要的角色,但模型的複雜度常導致條件尾部期望值與尾部機率的計算不具有封閉解,傳統上大多仰賴蒙地卡羅模擬法以得到其估計量。然而若對於估計精確度的要求更為嚴格時,則蒙地卡羅法將會耗費大量的計算時間。為了改善蒙地卡羅法的有效性,本研究提出一個基於指數截斷分佈的序貫重點抽樣估計方法,並透過理論證明所提出的估計量在計算尾部機率與條件尾部期望值時具有不偏性及具備較傳統蒙地卡羅估計量有效的性質。模擬研究以計算自正則檢定統計量的p值為例,實證研究則在GARCH模型的假設下,計算2014年1月2日至2015年1月6日期間的香港恆生指數與標準普爾500指數的多步期望損失,分別比較本文所提出的方法及蒙地卡羅法在計算尾部機率與條件尾部期望值的數值結果。模擬和實證研究的結果指出本文所提出的估計方法能有效的提升計算條件尾部期望值與尾部機率的速度,尤其當所計算的事件發生機率較小或檢定統計量所包含的隨機變數個數較少時,提升效果更為顯著。 Conditional tail expectation (CTE) and tail probability (TP) of a function of random variables play important roles in many applications. However, the CTE and TP usually have no closed form solution if complex stochastic models are employed and people rely on Monte Carlo (MC) simulation to estimate the CTE and TP. The MC method is usually time consuming if high accuracy of the approximation is demanded. In order to improve the efficiency of the MC estimator, this study proposes a sequential importance sampling scheme on the basis of truncated exponential distribution. The proposed estimator is proved to be unbiased and more efficient than the the MC estimator for computing the CTE and TP. Simulation study uses the estimation of the p-value of a self-normalized test statistic as an example for computing TP. Empirical study applies the proposed method to the multi-step prediction of expected shortfalls for the HSI and the S&P500 indices during January 2, 2014 and January 6, 2015 under GARCH framework. Simulation and empirical findings indicate that the proposed method is capable of computing the CTE and TP efficiently, especially when the probability of tail event decreases or the number of components of the test statistic decreases.

估計隨機向量函數條件尾部期望值之重點抽樣法 = An Importance Sampling of Conditional Tail Expectations for Functions of Random Variables
林, 家嬅

估計隨機向量函數條件尾部期望值之重點抽樣法 = An Importance Sampling of Conditional Tail Expectations for Functions of Random Variables / 林家嬅撰 - 高雄市 : 國立高雄大學, 2015[民104]. - 29葉 ; 圖 ; 30公分.
107年11月1日公開參考書目：葉29.
條件尾部期望值conditional tail expectation

估計隨機向量函數條件尾部期望值之重點抽樣法 = An Importance Sampling of Conditional Tail Expectations for Functions of Random Variables
LDR:03762nam0a2200277 450 001 458362
005 20190102102553.0
010 0 $b 精裝
010 0 $b 平裝
100 $a 20151007d2015 k y0chiy50 e
101 1 $a chi $d chi $d eng
102 $a tw
105 $a a am 000yy
200 1 $a 估計隨機向量函數條件尾部期望值之重點抽樣法 $d An Importance Sampling of Conditional Tail Expectations for Functions of Random Variables $z eng $f 林家嬅撰
210 $a 高雄市 $c 國立高雄大學 $d 2015[民104]
215 0 $a 29葉 $c 圖 $d 30公分
300 $a 107年11月1日公開
300 $a 參考書目：葉29
314 $a 指導教授：黃士峰教授
328 $a 碩士論文--國立高雄大學統計學研究所碩士班
330 $a 計算一隨機向量之函數的條件尾部期望值與尾部機率在應用領域上都扮演重要的角色,但模型的複雜度常導致條件尾部期望值與尾部機率的計算不具有封閉解,傳統上大多仰賴蒙地卡羅模擬法以得到其估計量。然而若對於估計精確度的要求更為嚴格時,則蒙地卡羅法將會耗費大量的計算時間。為了改善蒙地卡羅法的有效性,本研究提出一個基於指數截斷分佈的序貫重點抽樣估計方法,並透過理論證明所提出的估計量在計算尾部機率與條件尾部期望值時具有不偏性及具備較傳統蒙地卡羅估計量有效的性質。模擬研究以計算自正則檢定統計量的p值為例,實證研究則在GARCH模型的假設下,計算2014年1月2日至2015年1月6日期間的香港恆生指數與標準普爾500指數的多步期望損失,分別比較本文所提出的方法及蒙地卡羅法在計算尾部機率與條件尾部期望值的數值結果。模擬和實證研究的結果指出本文所提出的估計方法能有效的提升計算條件尾部期望值與尾部機率的速度,尤其當所計算的事件發生機率較小或檢定統計量所包含的隨機變數個數較少時,提升效果更為顯著。 Conditional tail expectation (CTE) and tail probability (TP) of a function of random variables play important roles in many applications. However, the CTE and TP usually have no closed form solution if complex stochastic models are employed and people rely on Monte Carlo (MC) simulation to estimate the CTE and TP. The MC method is usually time consuming if high accuracy of the approximation is demanded. In order to improve the efficiency of the MC estimator, this study proposes a sequential importance sampling scheme on the basis of truncated exponential distribution. The proposed estimator is proved to be unbiased and more efficient than the the MC estimator for computing the CTE and TP. Simulation study uses the estimation of the p-value of a self-normalized test statistic as an example for computing TP. Empirical study applies the proposed method to the multi-step prediction of expected shortfalls for the HSI and the S&P500 indices during January 2, 2014 and January 6, 2015 under GARCH framework. Simulation and empirical findings indicate that the proposed method is capable of computing the CTE and TP efficiently, especially when the probability of tail event decreases or the number of components of the test statistic decreases.
510 1 $a An Importance Sampling of Conditional Tail Expectations for Functions of Random Variables $z eng
610 # 0 $a 條件尾部期望值 $a 多步預測 $a 自正則檢定統計量 $a 序貫重點抽樣法 $a 尾部機率
610 # 1 $a conditional tail expectation $a multi-step prediction $a self-normalized test statistic $a sequential importance sampling $a tail probability
681 $a 008M/0019 $b 343201 4434 $v 2007年版
700 1 $a 林 $b 家嬅 $4 撰 $3 709606
712 0 2 $a 國立高雄大學 $b 統計學研究所碩士班 $3 769419
801 0 $a tw $b NUK $c 20181115 $g CCR
856 7 # $u https://hdl.handle.net/11296/gs9a52 $z 電子資源 $2 http