第一章 緒論。本篇論文之目的乃是利用拔靴法（Bootstrap） 以求穩健估計量之變 異數，並配合其化枋法比較評估之。此章就整篇論文的結構及內容做一般性的敘述。 第二章 簡介拔靴法。本章討論拔靴法的基本理論及其應用與結果等。 第三章 穩健估計量。本章介紹數類位置穩健估計量之性質與求法，緒如修剪平均值 、Ｍ估計量、有序統計量之線性組合等。 第四章 計算機模擬。本章就指數、常態、歪布、伽瑪四個母體分配，利用拔靴法及 其他方法配合電腦模擬，分別求出十種穩健估計量的變異數。 第五章 比較及結論。

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.

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.