Lucas(1976) 批評當時總體時間序列的計量分析方法，且主張傳統計量模型參數會隨體制及政策而改變，基於這些評論，於是許多對。嗜好(Taste)"及"技術"(Technology)" 結構參數估計的進論方法偭開始使用動態模型中的尤拉最適化條件(Euler Optimality Conditios)來進行估計。 然而，其中以Hansen(1982)所提出來的一般化動差估計法(Generalized Method of Moments)（簡稱GMM）最受矚目。此法乃源於一般化工具變數(GIVE)，在不需強烈假設下進行估計。其估計過程大致可分為下列三個階段： 1.建立正交化條件え建立目標函數最小化2.過度確認限制(overidentifying restriction) 之檢定問題因其本身即涵蓋許多估計式，如GIVE，MLE，2SLS， 且能滿足有限樣本性質，快速數斂。此法目前已用於總體計量，非線性理性預期實證及財務金融計量上。而本文應用台灣總體時間序列於資產訂價模型的GMM參數估計過程，證明了資料的適用性。另外，蒙地卡羅(Monte Carlo) 實驗設計模擬亦應用在本文研究，來探討有限樣本下的統計量之行為，並獲致適當的推論。 / Lucas(1976) criticized the existing strategies for econometricic analysis of macroeconomic time series and argues that papameters of traditional econometric models are not invariant with respect to shifts in policy regimes. In response to that criticism, several inference strategies for "taste and technology" structural parameter models using Euler optimality conditions in dynamic models were suggested. Hansen's(1982) Generalized Method of Moments(henceforth GMM) instrumental variables procedure is among the most notable inference strrategies for structural parameters. The procedure of GMM may consist three steps: (l)Set-up of the orthogonality conditions (2).Minimizing the objective function. (3)Test of the overidentifying restrictions In this paper we can understand the statistical properties of GMM estimator of Consumption-Based structural parameters obtained from Capital Asset Pricing Model by the use of Monte Carlo Simualtion .

本研究嘗試探討國小學童機率判斷能力的發展，想知道是否使用直接估計的方式來增加機率判斷的正確性。其中二個主要的獨變項是：年齡及作業方式，所抽取的三個年齡組分別是國小一、三、五年級的學童，而作業方式則以是否在作機率判斷前對機率的大小作直接估計分成：「量尺估計選擇作業」及「選擇作業」。希望藉由上述變項來了解直接估計方法能否增加國小學童機率判斷的正確性，以及這種直接估計的方法對不同年齡學童的助益是否有所差異。 研究設計採二因子的受試者間設計，研究對象是國小一、三、五年級的學童共96人，以個別施測的方式進行，每名受試都必須接受18個二選一的機率判斷題目，這些題目分由機率差異量大及機率差異量小二部分組成。實驗情境是以故事的方式呈現，要求受試機率題目作大小的判斷並說明判斷的理由。 根據二因子變異數分析結果如下： (1) 機率差異量大時： a)不同年級的學童在機率判斷的表現會不同，其中五年級的表現優於一年級的學童。 b)國小一年級的學童在「量尺估計選擇作業」的表現較「選擇作業」佳。 c)國小三年級的學童在「量尺估計選擇作業」的表現較「選擇作業」略佳。 d)國小五年級的學童在「量尺估計選擇作業」的表現較「選擇作業」相同。 (2) 機率差異量大時： a)不同年級的學童在機率判斷的表現會不同，其中五年級的表現優於一年級的學童。 b)國小一年級的學童在「量尺估計選擇作業」的表現和「選擇作業」一致。 c)國小三年級的學童在「量尺估計選擇作業」的表現和「選擇作業」相同。 d)國小五年級的學童在「量尺估計選擇作業」的表現和「選擇作業」沒有差異。

傳統的迴歸係數估計式為最小二乘法估計式，受自變數間共線性的影響很大。當自變 數間之共線性影響愈大時，則自變數與因變數間之關係愈趨於不穩定，且最小二乘法 估計式之變異數增大，致使模型喪失所應具備的解釋能力。因此荷肯（Hoerl, Kenn- ard ）二氏於一九七○年提出脊估計式，以改善最小二乘法估計式受共線性影響的缺 點。脊估計式與最小二乘法估計式的最大不同，在於脊估計式中多了一個大於零的常 數。 第一章為緒論。 第二章說明共線性產生的原因及其影響，進而推演出脊估計式的理論基礎及其幾何意 義；包括脊估計式的偏誤、期望值、變異數、均方誤差及脊估計式與最小二乘法估計 式的關係。 第三章脊估計式與其他估計式的比較，包括最小二乘法估計式、主成分估計式、等比 例縮小估計式，均以均方誤差作為其比較的標準。 第四章討論各種k 值的決定方法及其模擬結果。包括脊軌法，荷肯二氏反覆計算法， 直接脊估計式法，McDonald & Galarneau脊估計式法。 第五章綜合以上各章的結果，並就個人的觀點，比較第四章中各種k 值的決定法。

本文主旨在研究線性回歸模式中，若殘差之變異數並非一致時，如何作估計？同時如 何檢定母體是否具有不等變異性，其結構如下： 第一章：緒論。 第二章：估計之一般理論。第一節–基本定義。第二節－不偏性。第三節－一致性。 第四節－有效性。 第三章: 估計。第一節－迴歸係數之估計。第二節－殘差變異之估計。 第四章：檢定。第一節–巴萊特檢定。第二節–高、肯氏（GOLDFELD–QUANDT）檢定 。第三節–葛氏（GLEJSER ）檢定。 第五章：結論。

自1999年以來，台灣汽車車體損失險的投保率下降且損失率逐年上升，與強制第三責任險損失率逐年下降形成強烈對比，理論上若按個人風險程度計收保費，吸引價格認同的被保險人加入並對高風險者加費，則可提高投保率並且確保損失維持在合理範圍內。基於上述背景，本文採用國內某產險公司1999至2002年汽車車體損失保險資料為依據，探討過去保費收入與未來賠款支出的關係，在滿足不偏性的要求下，尋求降低預測誤差變異數的方法。 研究結果顯示：車體損失險存在保險補貼。以最小誤差估計法計算的新費率，可以改善收支不平衡的現象，但對於應該減費的低風險保戶，以及應該加費的高高風險保戶，以類神經網路推計的加減費系統具有較大加減幅度，因此更能有效的區分高低風險群組，降低不同危險群組間的補貼現象，並在跨年度的資料中具有較小的誤差變異。 / In the past five years, the insured rate of Automobile Material Damage Insurance (AMDI) has been declined but the loss ratio is climbing, in contrast to the decreasing trend in the loss ratio of the compulsory automobile liability insurance. By charging corresponding premium based on individual risks, we could attract low risk entrant and reflect the highly risk costs. The loss ratio can thus be modified to a reasonable level. To further illustrate the concept, we aim to take the AMDI to study the most efficient estimator of the future claim. Because the relationship of loss experience (input) and future claim estimation (output) is similar to the human brain performs. We can analyze the relation by minimum bias procedure and artificial neural network, reducing error with overall rate level could go through with minimum error of classes or individual, demonstrated using policy year 1999 to 2002 data. According to the thesis, cross subsidization exists in Automobile Material Damage Insurance. The new rate produced by minimum bias estimate can alleviate the unbalance between the premium and loss. However the neural network classification rating can allocate those premiums more fairly, where ‘fairly’ means that higher premiums are paid by those insured with greater risk of loss and vice-versa. Also, it is the more efficient than the minimum bias estimator in the panel data.

本篇論文在結構性時間序列模型基礎下，將中國大陸29省市自治區1978-2005年實質人均GDP，拆解出其長期趨勢變動軌跡中的水準值與斜率值，對照傳統上直接利用實質所得數據，以動態縱橫資料方法進行經濟成長條件收斂假說的檢定。本文特色在於加入潛在GDP長期趨勢項的水準值和斜率值，並利用內生解釋變數落後項動態分析。除可驗證隨著時間經過，中國相對貧窮省區是否終將逐漸趕上相對富有省份所得水準外，其次，根據GDP趨勢項一階與二階條件的收斂與否，可進而確認實質GDP收斂的本質。 我們發現，實質人均GDP收斂的本質關鍵在於潛在趨勢水準收斂，潛在GDP趨勢斜率的成長率將左右區域間實質所得收斂速度。大部分樣本中，擴大的Solow模型或考慮不同經濟開放程度因素下的內生成長模型，支持條件收斂假說，而後者設算出的收斂係數明顯較為低。此外，考慮採用Arellano and Bond(1991)的the first difference GMM估計式可能存在弱工具性問題(a weak instruments problem)，以Blundell and Bond(1998)發展出的the system GMM估計式，作為探討初始所得與經濟成長收斂的關係應是較為適合的方法。 / This research examines the economic growth conditional convergence hypothesis. Using the data of 29 provinces in Mainland China between 1978 and 2005, this study applied the structural time series model to deconstruct the provinces’ real GDP per capita into two parts - the level and the slope of trend movement. The characteristics of this paper are to include the level and the slope of trend of potential GDP and to consider the lagged dependent variables into the panel data. This study intends to validate whether the income level of relatively poor provinces will gradually catch up that of the relatively affluent provinces in Mainland China eventually. In addition, this study, based on the convergence or divergence in the first-order and second-order conditions of GDP tendency, will confirm the essence of the convergence in real GDP. The findings are that the essential key of the convergence in real GDP per capita is the convergence of the potential level of GDP. The growth of potential GDP tendency slope would affect the converging speed of real income in regions. The testing results of either the augmented Solow model or the endogenous growth model which considered different economic opening degrees both support the conditional convergence hypothesis in most sample sets, while the estimated convergence coefficients of the later are significantly lower than those of the former. In addition, considering the possible weak instruments problem in the first difference GMM estimator developed by Arellano and Bond (1991), the system GMM developed by Blundell and Bond (1998) should be a more suitable way to observe the relation between initial income level and economic growth convergence.

本研究以Schwartz與Moon（2000）提出的實質選擇權模型為基礎，再引入模糊理論，建立模糊實質選擇權模型。太陽能產業的益通為樣本公司，進行參數估計，並使用蒙地卡羅模擬，估計益通的合理價值。經過敏感度分析更進一步瞭解，影響公司價值最重要的因子為期初收入成長率與成本。 將本模型應用到其他電子產業，發現公司的股價常有遭到市場高估或低估，而偏離真實價值的情形發生。因此本研究建立一套投資策略，並參考模型估計的合理價格為投資的依據，希望能夠賺取價差。策略模擬的結果，獲利能力明顯優於長期持有的方式，也證明了本模型的實用性。 / In this study, we use the real option model from Schwartz and Moon (2000) as the basis, and then combine it with fuzzy theory to create Fuzzy Real Option Model. This study takes one company in solar power industry － E-TON as the sample company to conduct the parameter estimation. We also adopt the Monte Carlo Simulation method to assess the reasonable value of E-TON. After the sensitivity analysis, the results show that initial rate of growth in revenues and cost are the most important factors which influenced on the value of a company. Furthermore, we apply this model to other companies in electronics industry and discover that the stock prices are often overvalued or undervalued by the market. Therefore, we develop a set of investment strategies for people who want to make profits from the difference of prices. The result of strategic simulation shows that profit is apparently better than the way of buying and holding, and it proves the practicability of this model as well.

本研究採用Lee 和Poon 所提出的隱藏常態變數模型來估計混合連續與間斷型變數之參數估計，並估計其馬式距離。此外，並利用穩健估計來估計混合型資料參數及其馬式距離，可在有離群值時解決最大蓋似估計的不穩定。 / Poon and Lee (1987) applied normal latent variable model to deal with the parameters estimation for the data mixed with continuous and discrete variables and Bedrick et al. (2000) used this idea to evaluate the Mahalanobis distance. In this thesis, we extend a similar idea to robustly estimate Multivariate Data Mixed with Continuous and Discrete Variables with the same model. Furthermore, we evaluate the Mahalanobis distance which can determine similarity of variables. The proposed method can overcome the unreliability of MLE while there exist outliers in the data.

近幾年來，國人自殺死亡率不斷提高，且自殺死亡從1997年起已連續多年列於國人十大死亡原因之一，所以自殺防治工作刻不容緩。本研究採用自殺防治中心在桃園縣六家居家服務單位(龍祥、中國、仁愛、紅十字、家輔及寬福)所做之問卷調查資料，目的在於找出何種特性者，BSRS5 (The Five-Item Brief Symptom Rating Scale)分數及自殺意念分數可能較高。本研究屬於時序性追蹤資料，自民國96年5月份起，由居服人員針對受測對象進行訪談，大約每隔兩週收集一次，總共進行四次。 針對問卷進行基本敘述性統計、單項排名分析以及交叉分析後發現，在人口特質方面，男女性比例相當，年齡層主要皆在65~84歲，教育程度以不識字及國小為主；在BSRS5五題排名方面，以第一題「睡眠困難(難以入睡或早醒)」的平均分數最高，第四題「覺得比不上別人」平均分數最低；由交叉分析的結果發現身體狀況為一個重要的變數，身體狀況差的人BSRS5總分6分以上或自殺意念2分以上明顯較多。 對資料配適廣義估計方程式及Alternating Logistic Regressions的結果，發現在反應變數為BSRS5總分時，女性、身體狀況差及曾經看過精神科者BSRS5分數達到6分以上的可能性較高。若反應變數為自殺意念時，無論是利用廣義估計方程式或Alternating Logistic Regressions，從模型配適的結果發現只有BSRS5的效應顯著。不管利用BSRS5總分或是各題分開來看，BSRS5對自殺意念是一個相當有效的檢測工具，BSRS5分數愈高則自殺意念2分以上的機會也愈高。此外利用多層結構分析方法配適廣義估計方程式，針對BSRS5與受測次數間的關聯性分析，發現與配適傳統unstructured相關性矩陣的估計結果差異不大，但是可以減少許多參數估計，並且在電腦計算時間上是較快速的。 / In Taiwan, suicide has been among the top ten causes of death since 1997, and suicide prevention has thus attracted much attention since. Using the data provided by Taiwan Suicide Prevention Center (TSPC), this study is aimed to find out possible personal characteristics that might have some impacts on the BSRS5 (the Five-Item Brief Symptom Rating Scale) and suicide ideation scores The data come from a longitudinal study in which subjects from six elderly home service centers in Taoyuan County, Taiwan were visited four times between May and July, 2007, about two weeks between each visit. The total number of subjects is 1981. The proportions of male and female are nearly the same, the age range is from 65 to 84, and most of them have only an elementary school degree. Preliminary analyses indicate that among the five items in BSRS5, insomnia (the first item) is ranked the highest, and inferiority (the fourth item) is the lowest. In addition, health status is highly correlated to the BSRS5 and suicide ideation scores, the worse the health status, the higher the BSRS5 and suicide ideation scores. Fitting the data with Generalized Estimating Equation (GEE) and Alternating Logistic Regressions models with respect to the BSRS5 score, we further find that female, those who have bad health status, and those who have ever consulted a psychiatrist have higher probability that the BSRS5 score is greater than 6. As far as the suicide ideation score is concerned, the BSRS5 score is the only covariate that is statistically significant, an indication that BSRS5 is a useful tool for screening subjects at risk of committing suicide. While the conclusions stay the same whether the data are analyzed through GEE with commonly used unstructured correlation structure or newly developed multiblock and multilayer correlation structure, the latter approach reduces the computer time significantly.

20世紀以來，因為衛生醫療等因素的進步，各年齡死亡率均大幅下降，使得平均壽命大幅延長。壽命延長的效果近年逐漸顯現，其中的人口老化及其相關議題較受重視，因為人口老化已徹底改變國人的生活規劃，死亡率是否會繼續下降遂成為熱門的研究課題。描述死亡率變化的模型很多，近代發展的Age–Period–Cohort模型(簡稱APC模型)，同時考慮年齡、年代與世代三個解釋變數，是近年廣受青睞的模型之一。這個模型將死亡率分成年齡、年代與世代三個效應，常用於流行病學領域，探討疾病、死亡率是否與年齡、年代、世代三者有關，但一般僅作為資料的大致描述，本研究將評估APC模型分析死亡率的可能性。 APC模型最大的問題在於不可甄別(Non–identification)，即年齡、年代與世代三個變數存有共線性的問題，眾多的估計APC模型參數方法因應甄別問題而生。本研究預計比較七種較常見的APC模型估計方法，包括本質估計量(IE)、限制的廣義線性模型(cglim_age、cglim_period與cglim_cohort)、序列法ACP、序列法APC與自我迴歸模型(AR)，以確定哪一種估計方法較為穩定，評估包括電腦模擬與實證分析兩部份。 電腦模擬部份比較各估計方法，衡量何者有較小的年齡別死亡率及APC參數的估計誤差；實證分析則考慮交叉分析，尋找用於死亡率預測的最佳估計方法。另外，也將以蒙地卡羅檢驗APC的模型假設，以確定這個模型的可行性。初步研究發現，以台灣死亡資料做為實證，本研究考量的估計方法在估計年齡別死亡率大致相當，只是在年齡–年代–世代這三者有不同的詮釋，且模型假設並非很符合。交叉分析上，Lee–Cater模型及其延展模型相對於APC模型有較小的預測誤差，整體顯示Lee–Cater 模型較佳。 / Since the beginning of the 20th century, the human beings have been experiencing longer life expectancy and lower mortality rates, which can attributed to constant improvements of factors such as medical technology, economics, and environment. The prolonging life expectancy has dramatically changed the life planning and life style after the retirement. The change would be even more severe if the mortality rates have larger reduction, and thus the study of mortality become popular in recent years. Many methods were proposed to describe the change of mortality rates. Among all methods, the Age-Period-Cohort model (APC) is a popular method used in epidemiology to discuss the relation between diseases, mortality rate, age, period and cohort. Non-identification (i.e. collinearity) is a serious problem for APC model, and many methods used in the procedure included estimation of parameter. In the first part of this paper, we use simulation compare and evaluate popular estimation methods of APC model, such as Intrinsic Estimator (IE), constrained of age, period and cohort in the Generalized Linear Model (c–glim), sequential method, and Auto-regression (AR) Model. The simulation methods considered include Monte-Carlo and cross validation. In addition, the morality data in Taiwan (Data sources: Ministry of Interior), are used to demonstrate the validity and model assumption of these methods. In the second part of this paper, we also apply similar research method to the Lee-Carter model and compare it to the APC model. We found Lee–Carter model have smaller prediction errors than APC models in the cross–validation.