距離期望值4至6倍標準差以外的罕見機率電流值，是當前積體電路設計品質的關鍵之一，但隨著精確度的標準提升，實務上以蒙地卡羅方法模擬電路資料，因曠日廢時愈發不可行，而過去透過參數模型外插估計或迴歸分析方法，也因變數蒐集不易、操作電壓減小使得電流值尾端估計產生偏差，上述原因使得尾端電流值估計困難。因此本文引進統計方法改善罕見機率電流值的估計：先以Box-Cox轉換觀察值為近似常態，改善尾端分配值的估計，再以加權迴歸方法估計罕見電流值，其中迴歸解釋變數為Log或Z分數轉換的經驗累積機率，而加權方法採用Down-weight加重極值樣本資訊的重要性，此外，本研究也考慮能蒐集完整變數的情況，改以電路資料作為解釋變數進行加權迴歸。另一方面，本研究也採用極值理論作為估計方法。 本文先以電腦模擬評估各方法的優劣，假設母體分配為常態、T分配、Gamma分配，以均方誤差作為衡量指標，模擬結果驗證了加權迴歸方法的可行性。而後參考模擬結果決定篩選樣本方式進行實證研究，資料來源為新竹某科技公司，實證結果顯示加權迴歸配合Box-Cox轉換能以十萬筆樣本數，準確估計左、右尾機率10^(-4) 、10^(-5)、10^(-6)、10^(-7)極端電流值。其中右尾部分的加權迴歸解釋變數採用對數轉換，而左尾部分的加權迴歸解釋變數採用Z分數轉換，估計結果較為準確，又若能蒐集電路資訊作為解釋變數，在左尾部份可以有最準確的估計結果；而篩選樣本尾端1%和整筆資料的方式對於不同方法的估計準確度各有利弊，皆可考慮。另外，1%門檻值比例的極值理論能穩定且中等程度的估計不同電壓下的電流值，且有短程估計最準的趨勢。 / To obtain the tail distribution of current beyond 4 to 6 sigma is nowadays a key issue in integrated circuit (IC) design and computer simulation is a popular tool to estimate the tail values. Since creating rare events via simulation is time-consuming, often the linear extrapolation methods (such as regression analysis) are applied to enhance efficiency. However, it is shown from past work that the tail values is likely to behave differently if the operating voltage is getting lower. In this study, a statistical method is introduced to deal with the lower voltage case. The data are evaluated via the Box-Cox (or power) transformation and see if they need to be transformed into normally distributed data, following by weighted regression to extrapolate the tail values. In specific, the independent variable is the empirical CDF with logarithm or z-score transformation, and the weight is down-weight in order to emphasize the information of extreme values observations. In addition to regression analysis, Extreme Value Theory (EVT) is also adopted in the research. The computer simulation and data sets from a famous IC manufacturer in Hsinchu are used to evaluate the proposed method, with respect to mean squared error. In computer simulation, the data are assumed to be generated from normal, student t, or Gamma distribution. For empirical data, there are 10^8 observations and tail values with probabilities 10^(-4),10^(-5),10^(-6),10^(-7) are set to be the study goal given that only 10^5 observations are available. Comparing to the traditional methods and EVT, the proposed method has the best performance in estimating the tail probabilities. If the IC current is produced from regression equation and the information of independent variables can be provided, using the weighted regression can reach the best estimation for the left-tailed rare events. Also, using EVT can also produce accurate estimates provided that the tail probabilities to be estimated and the observations available are on the similar scale, e.g., probabilities 10^(-5)~10^(-7) vs.10^5 observations.

在測驗含有題組(testlet)結構時，由於違反了試題反應理論(Item Response Theory, IRT)中局部獨立性的假設，使得IRT的估計方法產生偏誤，過去研究的解決方式為在IRT模型中多加入一個參數，將題組的影響力納入模型中，此即為題組反應理論(Testlet Response Theory, TRT)，在貝氏(Bayesian)的架構下，此方法的計算則可透過SCORIGHT軟體來達成。本研究旨在透過另一種方法，即廣義方程式(Generalized Estimation Equation, GEE)去處理測驗中的題組效果。GEE過去常被使用於分析縱貫式(longitudinal)的資料，本研究使用此方法來捕捉題組測驗下作答結果的相關性，並經重新參數化調整係數後使其能對受試者能力值進行估計。 電腦模擬的結果顯示GEE能有效的處理題組效果帶來的影響。在GEE和貝氏題組模型的比較上，GEE對於程度好和程度差的受試者有較佳的估計效果；而貝氏題組模型則對於程度中等的受試者表現較好，此外我們也針對GEE的估計效率進行了實驗，結果顯示先將受試者依能力分組再進行GEE估計能提升GEE的估計效率。 在文章中，我們也展示了使用GEE計算題組訊息量的方式，做為題組式測驗下評估該測驗對於各能力區間的受試者在估計準確度上的參考。 / If the tests have testlet structure, the bias may arise when using traditional Item Response Theory(IRT) estimation methods due to the violations to the assumption of local independence. To deal with the testlet effect, previous studies introduced a new parameter to the classical IRT model which called Testlet Response Theory(TRT). Under the Bayesian framework, the estimation can be accomplished on the SCORIGHT program. The purpose of this paper is to use another method named Generalized Estimation Equation(GEE) to model testlet response data. GEE was commonly used to analyze the longitudinal data. We use this method to capture the information from the correlated items and estimated ability of the examinees through re-parametrization. Simulation results indicate that GEE can deal with the testlet effect effectively. On the comparison between GEE and Bayesian testlet model, GEE does better on estimation of the examinees who have high or low ability level. In contrast, Bayesian testlet model does better on estimation of medium ability level. In addition, we design the experiment to test the efficiency of GEE. The results show that group the examinees according to their ability before doing the GEE estimation can improve the efficiency of GEE. In this paper, we also demonstrate the method to calculate testlet information using GEE which can be taken as reference for assessing estimation accuracy of each ability level in testlet-based testing.

近期關於組織目標的研究指出，傳統以營利為目的的公司，隨著政府與大眾對於社會議題的日益關注而開始履行企業社會責任；另一方面，傳統以解決社會問題為目的的非營利組織，為了處理資金問題而開始從事營利行為。因為營利與非營利組織的分界開始模糊，各種混合型態的組織跟著出現，構成了一個組織目標的光譜。然而，這個概念上的目標光譜並不容易呈現，目前針對社會價值的創造(Social Value Creation，簡稱SVC)在量化上的分析成果亦有限。本研究從產業經濟學的混合寡占理論出發，提出一個「SVC投資市場」以衡量組織對於社會價值的重視程度，並使用觀察到的資料描繪出SVC投資市場中的需求。再透過組織目標函數的設定以及在市場中競爭的結果，推估組織考量社會價值的比重，找出組織在目標光譜中的位置。本研究針對台灣上市公司的企業社會責任報告書資料以及財報資料進行分析後發現，目前台灣上市公司的消費者並不太重視公司的SVC活動。政府若欲提升公司對於SVC的重視程度，可以嘗試藉由改變消費者的購買決策來影響公司的目標決策。

近紅外線影像由於其物理特性與成像方式，其紋理細節都有發散模糊不清的現象，對於以紋理為主要特徵的年齡辨識問題而言更具挑戰。本論文主要目的是以近紅外線人臉影像為基礎，找出對近紅外線年齡特徵有最佳描述力的特徵描述子，辨識近紅外線影像中被拍攝者的年齡區間，建構整個年齡層估算機制。 相關研究一部分關注可見光年齡辨識，另一部分則聚焦在近紅外線人臉辨識，目前還沒有近紅外線年齡辨識的相關文獻能參考，如何從接近的研究領域找尋是適當的演算法是本研究遇到的第一個挑戰。在資料庫的部分，FGNET和MORPH常被用於可見光的年齡辨識議題； PolyU和LDHF則用於近紅外線人臉辨識相關研究，在目前沒有近紅外線年齡資料庫的情況，本研究自建RSNIR（Intel RealSense Near-Infrared Age Database），因此如何標準化拍攝環境流程、蒐集穩定的近紅外線影像是本研究面臨的第二個挑戰。 區域性特徵擷取方法的關鍵在於特徵描述子的描述力。本研究以LBP（Local Binary Patterns）為基礎，探討LBP在內的24個特徵描述子，最後實驗測試各個描述子在RSNIR的辨識率，結果發現基本型Fuzzy LBP和擴充型RILBP對近紅外線年齡特徵有最佳描述力。在空間譜子區塊（patch）設計部分，以3x3切割子區塊數的辨識效果最好，反應出其與影像校正時的人臉影像空間定義方式有關。

This study examines the effects of market concentration on firm-level productivity using data on Chinese above-scale industrial firms from 2001 to 2007. Productivity is identified as total factor productivity (TFP) and estimated using the Olley-Pakes three-step estimation in order to avoid simultaneity and selection biases. Using data on around 590,000 industrial firms, empirical results indicate that the less concentrated the market, the higher the productivity generally. However, a few industries are identified to have opposite direction; that is, the more concentrated, the more productive are the firms. In some industries, there is no significant relationship between market concentration and firm productivity.

為了解在中國政府正式開始扶植中國半導體產業之後該產業生產率的動態變化，本研究以2001年至2007年之間中國半導體產業的企業層面資料為樣本範圍，並使用Olley和Pakes(1996)的三階段估計法對個別廠商生產率進行估計，同時有效解決傳統使用OLS方法估計生產率會產生的聯立性和樣本選擇問題。接著，再利用Melitz和Pakes(2015)年針對Olley和Pakes(1996)的模型加入廠商進退出市場決策之生產率動態分解模型，對兩兩年度的生產率變動進行拆解。有別於過去文獻主要以中國半導體產業的經營策略為主軸，敘述產業發展，或是使用其他計量方法推估廠商生產率而忽略廠商進出市場行為，本研究將受中國政府提供優惠政策而進入中國市場投資半導體產業和因經營方向不合時宜而遭市場淘汰退出的廠商行為納入考量，並試圖歸納2000年以來中國政府對半導體產業態度的轉變對於廠商生產率帶來的影響。 / The main purpose of the study is to examine the dynamics and decomposition of total factor productivity in China’s semiconductor industry after the government started to pour support and investment into the industry. This study uses firm-level financial and production data to estimate total factor productivity with Olley-Pakes estimation to eliminate both simultaneity problem and selection bias. Furthermore, it separates the contribution of firms to the aggregate productivity changes into three categories for surviving, entering, and exiting firms. Apart from studying merely business strategies, the research aims at taking entry and exit effects into account and also figuring out the impact of the policy of China’s government on the entire semiconductor industry since 2000.

在迴歸分析中，當資料中存在很多離群值時，偵測的工作變得非常不容易。 在此狀況下，我們無法使用傳統的殘差分析正確地偵測出其是否存在，此現象稱為遮蔽效應(The Masking Effect)。 而為了避免此效應的發生，我們利用最小中位數穩健迴歸估計值(Least Median Squares Estimator)正確地找出這些群集離群值，此估計值擁有最大即50﹪的容離值 (Breakdown point)。 在這篇論文中，用來求出最小中位數穩健迴歸估計值的演算法稱為步進搜尋演算法 (the Forward Search Algorithm)。 結果顯示，我們可以利用此演算法得到的穩健迴歸估計值，很快並有效率的找出資料中的群集離群值；另外，更進一步的結果顯示，我們只需從資料中隨機選取一百次子集，並進行步進搜尋，即可得到概似的穩健迴歸估計值並正確的找出那些群集離群值。 最後，我們利用鐘乳石圖(Stalactite Plot)列出所有被偵測到的離群值。 在多變量資料中，我們若使用Mahalanobis距離也會遭遇到同樣的屏蔽效應。 而此一問題，隨著另一高度穩健估計值的採用，亦可迎刃而解。 此估計值稱為最小體積橢圓體估計值 (Minimum Volume Ellipsoid)，其亦擁有最大即50﹪的容離值。 在此，我們也利用步進搜尋法求出此估計值，並利用鐘乳石圖列出所有被偵測到的離群值。 這篇論文的第二部分則利用變數轉換的技巧將迴歸資料中的殘差項常態化並且加強其等變異的特性以利後續的資料分析。 在步進搜尋進行的過程中，我們觀察分數統計量(Score Statistic)和其他相關診斷統計量的變化。 結果顯示，這些統計量一起提供了有關轉換參數選取豐富的資訊，並且我們亦可從步進搜尋進行的過程中觀察出某些離群值對參數選取的影響。 / Detecting regression outliers is not trivial when there are many of them. The methods of using classical diagnostic plots sometimes fail to detect them. This phenomenon is known as the masking effect. To avoid this, we propose to find out those multiple outliers by using a highly robust regression estimator called the least median squares (LMS) estimator which has maximal breakdown point. The algorithm in search of the LMS estimator is called the forward search algorithm. The estimator found by the forward search is shown to lead to the rapid detection of multiple outliers. Furthermore, the result reveals that 100 repeats of a simple forward search from a random starting subset are shown to provide sufficiently robust parameter estimators to reveal multiple outliers. Finally, those detected outliers are exhibited by the stalactite plot that shows greatly stable pattern of them. Referring to multivariate data, the Mahalanobis distance also suffers from the masking effect that can be remedied by using a highly robust estimator called the minimum volume ellipsoid (MVE) estimator. It can also be found by using the forward search algorithm and it also has maximal breakdown point. The detected outliers are then displayed in the stalactite plot. The second part of this dissertation is the transformation of regression data so that the approximate normality and the homogeneity of the residuals can be achieved. During the process of the forward search, we monitor the quantity of interest called score statistic and some other diagnostic plots. They jointly provide a wealth of information about transformation along with the effect of individual observation on this statistic.

本次研究使用全民健康保險研究資料庫2005承保抽樣歸人檔(LHID2005)，共40萬人的承保資料，針對肺癌患者的特徵進行分析，並與美國國家癌症研究所的肺癌資料作比較，罹患肺癌的人數都呈現男性多於女性，罹癌年齡的最高峰同樣落在65歲至74歲。 接著，將門診處方及治療明細檔和住院醫療費用清單明細檔進行彙整，整理出肺癌患者在2005年至2012年之間的門診費用以及住院費用，並比較不同項目的差距及特徵，門診費用以用藥明細點數最高，住院花費前五名的項目為葯費、病房費、放射線診療費、檢查費以及治療處置費。 最後，建構肺癌治療的多重型態模型，治療方式包含手術治療、放射線治療、化學治療，估計不同狀態之間的轉換力，進而算出五年定期躉繳肺癌保單之純保費。 / This study used Longitudinal Health Insurance Database 2005 (LHID2005) from Taiwan’s National Health Insurance Research Database (NHIRD). Screening the 400,000 insured of NHIRD to select the lung and bronchus cancer patients. This study analyzed and described their characteristics. Furthermore, it compared Taiwan’s lung and bronchus cancer data with the data in the United States derived from National Cancer Institute of the USA. The results revealed that the number of male patients is more than female patients and lung cancer is most frequently diagnosed among people aged 65-74 in both countries. Another aim was to sum up the lung cancer medical cost in 2005 to 2012 from NHIRD database, including ambulatory care expenditures by visits and inpatient expenditures by admissions. The highest cost of outpatients was medicine fee. The top five inpatient expenditures were medicine fee, ward fee, radiation therapy fee, inspection fee and therapeutic treatment fee. Finally, this study constructed a multiple state model of lung cancer treatment, including surgery, radiotherapy, chemotherapy. Estimating the transition intensities from multiple state model to calculate the pure premium of a five-year lung cancer policy.

資本資產定價模型 (CAPM) 由Sharp (1964)、Lintner (1965)及Black (1972)發展出後，近年來已被廣泛的應用於衡量證券之預期報酬率與風險間之關係。一般而言，衡量結果之估計有兩個階段，首先由時間序列分析估計出貝它(beta)係數，然後再檢定廠商或投資組合之平均報酬率與貝它係數之關係。 Fama與MacBeth (1973)利用最小平方法估計貝它係數，再將由橫斷面迴歸方法所得出之斜率係數加以平均後，以統計t-test檢定之。然而以最小平方法估計係數，其估計值很容易受離群值之影響，因此本研究考慮以穩健估計 (robust estimator)來避免此一問題。另外，本研究亦將長期資料分析 (longitudinal data analysis) 引入CAPM裡，期望能檢定貝它係數是否能確實有效地衡量出系統性風險。 論文中以台灣股票市場電子業之實證分析來比較上述不同方法對CAPM的結果，資料蒐集期間為1998年9月至2001年12月之月資料。研究結果顯示出，穩健估計相對於最小平方法就CAPM有較佳的解釋力。而長期資料分析模型更用來衡量債券之超額報酬部分，是否會依上、中、下游或公司之不同而不同。 / The Capital Asset Pricing Model (CAPM) of Sharp (1964), Lintner (1965) and Black (1972) has been widely used in measuring the relationship between the expected return on a security and its risk in the recent years. It consists of two stages to estimate the relationship between risk and expected return. The first one is that betas are estimated from time series regressions, and the second is that the relationship between mean returns and betas is tested across firms or portfolios. Fama and MacBeth (1973) first used ordinary least squares (OLS) to estimate beta and took time series averages of the slope coefficients from monthly cross-sectional regressions in such studies. However it is well known that OLS is sensitive to outliers. Therefore, robust estimators are employed to avoid the problems. Furthermore, the longitudinal data analysis is applied to examine whether betas over time and securities are the valid measure of risk in the CAPM. An empirical study is carried out to present the different approaches. We use the data about the Information and Electronic industry in Taiwan stock market during the period from September 1998 to December 2001. For the time series regression analysis, the robust methods lead to more explanatory power than the OLS results. The linear mixed-effect model is used to examine the effects of different streams and companies for the security excess returns in these data.

本文係針對臺灣50指數期貨與基金於2003年6月30日上市之後，臺灣期貨及現貨市場報酬率間領先落後關係與波動性的變化來進行探討。研究分為兩部份，第一部份是觀察臺灣50指數期貨與現貨之間的關聯性，並探討臺灣加權股價指數、金融保險類股股價指數及電子類股股價指數期貨與現貨市場間的變化；第二部份是採用可模擬現貨走勢的臺灣50指數基金、國泰金及臺積電的股價來做為現貨的替代變數，觀察其與期貨之間的關連性是否與第一部份的結果類似，若是實證結果極為相同，則相關機構與一般投資人將可運用各期貨與其標的指數中市值最大的股票來進行套利操作。此外，本文在進行模型估計時，首度採用一階段估計法，來聯合估計雙變量GARCH模型中的條件平均數方程式與條件變異數方程式，以避免過去相關文獻將兩條方程式個別估計時所造成的估計誤差。 實證結果所獲得的重要結論如下：首先，臺灣期貨市場的發展仍未趨成熟，並不具有價格發現的功能，在考慮風險溢酬方面，僅有臺灣50指數期貨與現貨的投資人會在報酬率之外，額外要求用以補償的風險溢酬，再者，臺灣50指數期貨與基金的上市，並沒有對臺灣現有的期貨與現貨市場造成顯著的影響，然而，替代變數並不能完全取代現貨指數，但相較之下，國泰金在臺灣50指數期貨與基金上市之後的那段期間模擬成效最好。 / This paper investigates the change of lead-lag relationship in returns and volatilities in Taiwan futures and spot markets after the introduction of Taiwan 50 Futures and Taiwan Top50 Tracker Fund (TTT) on June 30, 2003. The study divides into two parts. The first part examines the relationship between Taiwan 50 Futures and spot markets, and also discusses the change of Taiwan Stock Exchange Capitalization Weighted Stock Index, Taiwan Stock Exchange Banking and Insurance Sector Index, and Taiwan Stock Exchange Electronic Sector Index in futures and spot markets. Another part uses the stock price of TTT, Cathay Financial Holding Company and Taiwan Semiconductor Manufacturing Company as the substitutive variables of spot index and goes a step further to examine the relationships between them and futures individually. Additionally, this research used One-Pass Method for first time to estimate jointly the conditional mean equation and conditional variance equation of Bivariate GARCH Model to avoid estimating error in previous relative studies with Two-Pass Method. The major empirical results are as follows: first, the development of Taiwan futures market is incomplete. The futures market does not play the price discovery role to the spot market. Second, under the consideration of risk premium, only investors in Taiwan 50 Futures and spot markets would ask for compensated risk premium excepting returns. Third, the opening of Taiwan 50 Futures and TTT does not influence significantly Taiwan futures and spot markets. Last but not least, these substitutive variables can not replace spot index perfectly. However, comparing with others, the stock price of Cathay Financial Holding Company is the very model of Taiwan Stock Exchange Banking and Insurance Sector Index after the introduction of Taiwan 50 Futures and TTT.