本文主要的目的是藉由The Geometer's Sketchpad (GSP)軟體的設計，幫助我們得到一組連續型模糊樣本。另外對於模糊數的無母數檢定我們提供了一個較為一般的方法，可以針對梯型、三角型，區間型的模糊樣本同時進行處理。 藉由利用GSP. 軟體所設計的模糊問卷，可以較清楚地紀錄受訪者的感覺，此外我們所提供之對於模糊數的無母數檢定方法比其他方法較為有效力。 在未來的研究裡，我們仍有一些問題需要解決，呈述如下：當所施測的樣本數很大時，如何有效率的在網路上紀錄受測者所建構的隸屬度函數？ / The purpose of this paper is to develop a methodology for getting a continuous fuzzy data by using the software The Geometer's Sketchpad (GSP). And we propose a general method for nonparametric tests with fuzzy data that can deal with trapezoid, triangular, and interval-valued data simultaneously. Using the fuzzy questionnaire designed by GSP. can help respondents to record their thoughts more precisely. Additionally our method for nonparametric tests with fuzzy data is more powerful than others. Additional research issues for further investigation are expressed by question such as follows: how to record the membership function on line, especially when the sample size is large?

迴歸分析中，若變數間有非線性(nonlinear)的關係，此時我們可以用B-spline線性迴歸，一種無母數的方法，建立模型。Penalized spline是B-spline方法的一種改良，其想法是增加一懲罰項，避免估計函數時出現過度配適的問題。本文中，考慮三種方法:(a) Marginal Mixed Model approach, (b) Conditional Mixed Model approach, (c) 貝氏方法建立信賴帶，其中，我們對第一二種方法內的估計式作了一點調整，另外，懲罰項中的平滑參數也是我們考慮的問題。我們發現平滑參數確實會影響信賴帶，所以我們使用cross-validation來選取平滑參數。在調整的cross-validation下，Marginal Mixed Model的信賴帶估計不平滑的函數效果較好，Conditional Mixed Model的信賴帶估計平滑函數的效果較好，貝氏的信賴帶估計函數效果較差。 / In regression analysis, we can use B-spline to estimate regression function nonparametrically when the regression function is nonlinear. Penalized splines have been proposed to improve the performance of B-splines by including a penalty term to prevent over-fitting. In this article, we compare confidence bands constructed by three estimation methods: (a) Marginal Mixed Model approach, (b) Conditional Mixed Model approach, and (c) Bayesian approach. We modify the first two methods slightly. In addition, the selection of smoothing parameter of penalization is considered. We found that the smoothing parameter affects confidence bands a lot, so we use cross-validation to choose the smoothing parameter. Finally, based on the restricted cross-validation, Marginal Mixed Model performs better for less smooth regression functions, Conditional Mixed Model performs better for smooth regression functions and Bayesian approach performs badly.

隨著資訊科技的發展與網際網路的普及，音樂與電影光碟盜版的問題也逐年嚴重，然影音盜版不僅影響權利人團體，影音業者及創作者之生存，亦攸關我國智慧財產之發展，更常成為我國在國際貿易諮商上的重要課題。在種種緣由與現況下，得使國內許多產、官、學、研團體想去研究影音盜版的相關議題，以了解其嚴重程度如何，或有無較客觀合理的指標或評估方式?並進一步研擬有效方法來防範盜版問題進一步惡化，為此上述問題乃是本研究之源起。 目前所有的影音盜版研究，多著重在計算盜版率,探討盜版因素,盜版行為的心理與法制問題，皆還尚未針對影音盜版率，建構出可供學者推論的盜版率機率分配，及其他相關的數量研究，因此，本研究的主要實証方向，乃根據2004年經濟部智慧財產局(intellectual property office ministry of economic affairs,R.O.C)委託政治大學之消費者調查資料，就音樂CD、影音VCD/DVD兩部分，針對筆者有興趣之變項(性別、年齡、有無上網下載等)，(1)分別建構各自的混合分配並了解其分配間的差異與趨勢， (2)探討消費者對盜版行為的態度，(3)了解消費者對喜好的光碟所願付價格之差異，(4)建立盜版率分配的信賴帶，以及(5)針對現有的調查資料進行盜版辨別。 最後，就查緝盜版與維護智慧財產權兩方面，實證分析提供政府相關單位作為參考的依據，以求擬訂周詳且完善的措施來防範日益惡化的盜版問題。 / With the development of computer technology and widespread of internet, the piracy problem goes more serious. The piracy situation makes much influence not only on the rights of international oblige societies but also the growing of the intellectual properties in Taiwan. Moreover, it becomes the rock on the road of international commercial negotiations. Beyond the serious situation in the mean time, more researchers and relevant organizations on the island are trying to pay more attention to this important issue. This research intends to understand several questions: How is the actual situation on the piracy problem? Are there any objective evaluation ways? Are there any effective policies to prevent it from going deeper? These questions lead to this research. In the meantime, most of Audio & Video piracy research emphasized only on calculating the piracy rate, or the reasons, or the relevant psychological and law problems, but few on piracy quantitative studies. Therefore the mainly intention of this research is based on the data from the IPO(Intellectual Property Office Ministry of Economic Affairs, ROC), which is executing by National Chengchi University. As for the two parts concerning music CD and visual VCD/DVD, and the variables those I am highly interested including gender, age, education level, downloading or not. The empirical study results show as below: (1)The piracy rate distribution corresponds with the Mixed Model, that mean that it have been proportionally mixed two degenerate distribution (while X=0 and 100) with the Normal distribution. (2) On the facets of distribution differences and trends analysis, not only music CD and visual VCD/DVD, the results of the research by Mann-Whitney test and Kolmogorov-Smirnov two sample test both reveal the rising tendency of overall piracy rate. The generation of 20~29 years old is the mainly pirate group, moreover, higher education grades group does the more pirating behaviors, and lower income group intends more unauthorized copying conducts. Furthermore, along with the development of internet technology, the infringement behavior is more serious on the network connectors than the non-network downloaders. (3) Under surveying the opinions of consumers about the piracy, regardless of whether music or movies, the deviation is more serious on male than female, under 30-year-old than above, low educated than high, low income than high, pirate than non-pirate, downloaders than non-downloaders. The problem locates not only the lack of the concepts and recognition on the intellectual properties rights, but also the scarce of moral or legal limitations on the unauthorized rebuilding or downloading. But in the other curious facet, although the higher grade educated groups got more equitable standpoints on the piracy discussion, but evidenced depend upon the collected data they are also mainly the group who did the piracy behaviors more. (4) On the price range that a consumer would like to pay for, most of the pirate consumer tends to pay low price to buy the A/V goods, most of the non-pirating consumer group tends to pay general price to buy ones, and no significant difference of these two groups with high price, (5) On the facets of confidence bands on the whole music CD and visual VCD/DVD pirating rate, because of the specialties of pirating data- the higher frequency while the piracy rate values 0 and 100, so that the upper and lower bound reveals at 0 and 100. Futhermore, the confidence bands obtains from the population distribution function, therefore it’s suitable for the goodness-of-fit test. The results met the Kolmogorov-Smirnov one sample test. (6) On the data recognition facets, the logistic regression model of piracy is constructed in this research. Classification from the fitted logistic regression models, the results reveals 107 non-pirate are mis-judged to pirating behaviors, 186 pirating samples are neglected to non-pirate ones, the correct recognition rate goes high of 88 %. Key Words：Piracy Rate, Mixture Models, Mann-Whitney, Kolmogorov-Smirnov, Logistic Regression Model, Nonparametric Statistics.

一、研究動機與目的 本研究的目的，在於探討血壓胺在記憶上是扮演抑制或促進的角色，由於腦中的血壓 胺有百分之八十以上含量分佈在背縫核（B ７）和腹縫核（B ８），而投射到前腦， 背縫核大部份投射到紋狀體，腹縫核大部份投射到海馬迴，兩者在功能上有很多不一 樣的地方。因此，本實驗目的，在於分別破壞紋狀體、海馬迴和前腦中血壓胺的含量 ，來探討血壓胺在記憶上所扮演的角色。 二、研究方法 （一）實驗動物 實驗動物為９０隻雄性大白鼠。 （二）實驗程序 首先分成三個實驗進行，分別手術前腦、紋狀體、海馬迴三個區域。手術十天後，開 始進行實驗，分別給予電擊訓練後，馬上注射藥物至手術的區域，以破壞血壓胺的含 量，四十八小時後，測試大白鼠對於電擊的記憶，測試完畢之後，馬上將大白鼠犧牲 掉，分別取前腦、紋狀體、海馬迴、背縮核以及腹縫核的組織，以作組織化學分析。 （三）統計分析 （１）有關記憶的行為反應，以無母數統計方法進行分析。 （２）有關腦部血壓胺含量的分析，以單因子變異量的模式進行分析。 （四）預期實驗結果 （１）行為分析 破壞血壓胺組的大白鼠，其記憶行為反應較未破壞組的大白鼠差。 （２）組織化學分析 血壓胺的含量：背縫核較腹縫核多。未被破壞組較破壞組多。

對一個母體Ｆ（ｘ）來講，第Ｐ百分位數 就是使得Ｆ（Ｘｐ）＝Ｐ的點，而 的信 賴上、下限就對應到母體的容忍上、下限（Tolerance Limit Lower or Upper）ｒ＝ Ｐ（Ｕ Ｘｐ）or ＝Ｐ（Ｌ Ｘｒ）。古期的無母數作法是根據一個秩統計量（Or der Sta-＆ Koopman及Proschan分別提出不同的無母數方法，二者均是以秩統計量的 線性組合為主。唯Ｈ＆Ｋ的容忍上、下限限於Ψu、ΨL族群，而Ψu＝｛Ｆ：─log（ １－Ｆ）is convex），ΨL＝｛Ｆ：─log F is convex ）；Ｂ＆Ｐ的容忍下限作法 僅適是ＩＦＲ（Increasing Failure Rate） 而且Ｆ（０）＝０的族群。本論文以負 指數分配為母體在參合模式下，εＦ□＋（１－ε）Ｆ□來比較這兩種容忍上、上限 ，同時也覯察了若母體該是參合模式而誤採單一模式時所發生的偏差。 本論文計吊五章，第一章：緒論；第二章：古典的無母數方法；第三章：參合模式下 Hanson & Koopman的方法；第四章：參合模式下Barlow & Proschan 的方法；第五章 ：二種方法的分析比較。

在現代資產定價的研究中，短期利率扮演一個很重要的角色。短期利率模型中最重要的一類是連續時間的擴散模型(continuous-time diffusion model)。這些模型有一個特性：假設已知利率的動態過程，亦即對利率模型的漂移項及擴散項作特定函數型態假設，而並無完整的經濟理論說明為何如此設定。我們知道不同的利率模型設定會推導出不同的商品評價公式，因此任意函數型態的模型一旦設定偏誤太大，勢必對評價公式的準確性造成很大的影響。有鑑於此，近幾年來利用無母數統計方法來估計利率模型的文獻與日具增。因為利用無母數統計方法可以減少對利率模型的任意設定。 基於對短期利率模型任意參數設定的懷疑，以及欲探究台灣短期利率的動態過程究竟為何種型態，因此本文以Stanton(1997)的無母數統計法利率模型，以台灣貨幣市場30天期的商業本票利率資料作實證分析。而為了更清楚了解無母數法利率模型的表現，本文亦採用CKLS (1992)所發展的估計方法，以一般化動差法(Generalized method of moment, GMM)估計九個有參數利率模型，將所得到結果與無母數法的利率模型比較。最後，我們利用估計出的無母數利率模型來建構利率期間結構，並與實際資料作比較。 本文實證結果發現，台灣短期利率的動態過程不管是漂移項或擴散項函數皆呈現非線性型態，且漂移項函數呈現負斜率的均數回歸(mean reverting)現象，而擴散項函數大致是隨利率水準愈大而其數值亦愈大。因此若以非線性、具有均數回歸且擴散項是遞增的函數式來設定利率模型的參數，應該較能刻劃台灣短期利率動態過程。另外，從有參數模型的實證結果發現，漂移項或擴散項函數，只要其中一項設定有誤，不僅會使該項的預測能力變差，亦連帶會影響另一項的預測能力，進而也會影響模型的整體表現。這意味著以無母數方法來估計利率模型有其必要性。最後，我們利用無母數法利率模型所估計的利率期間結構與實際的資料比較，發現估計結果還算不錯。

本文將模糊理論的觀念，應用在估計、檢定及時間數列分析上。研究重點包括離散型及連續型模糊樣本的定義與度量，模糊參數的最佳估計，模糊排序方法應用於無母數檢定，模糊相似度的定義、性質，以及如何將其應用於辨識不同時間數列間的落差l期相似程度等。我們首先將常見的模糊資料分為離散型及連續型，並針對不同類型的資料，給定對應的模糊平均數、模糊變異數等模糊參數的概念與一些重要性質。接著我們提出幾種估計方法，針對不同的模糊參數進行最佳估計並提出可行的評判準則。進一步地，我們將模糊排序方法應用於無母數檢定推論。最後我們提出模糊相似度的定義與度量。經由系統性的模擬與分析，我們建立兩時間數列間模糊相似度演算法則。實證分析方面，我們利用提出的方法對台灣的股價加權指數、個股股價進行估計及檢定；同時，針對台灣歷年GDP、民間消費、毛投資間的相似性進行偵測，以驗證我們提出的模糊參數估計、模糊無母數檢定及模糊相似度演算法的效率性與實用性。 / In this paper, we apply fuzzy theory in estimation, nonparametric test, and time series analysis. Our focus is on: How to define and measure the discrete type fuzzy data and continuous one? How to find the optimal estimators for fuzzy parameters? How to apply fuzzy ranking methods in nonparametric test when the data is vague? How to define and find the degree of fuzzy similarity between two time series? First, fuzzy data is classified according to its type, discrete or continuous. Then we give some definitions and properties on fuzzy mean, fuzzy variance for different type of fuzzy data. Next, we proposed some estimating methods and evaluation rules. Moreover we apply fuzzy ranking methods in nonparametric test, such as Sign test, Wilcoxon signed rank test, Wilcoxon rank sum test, and so on. Finally, we suggest the definitions as well as the algorithm for computing the degree of fuzzy similarity between two time series. We also give some simulate and empirical examples to illustrate the techniques and to analyze fuzzy data. Results show that fuzzy statistics with soft computing are more realistic and reasonable for the social science research.

在過去研究犯罪經濟學的理論文獻上，失業率對各犯罪類型的影響為正向關係，但在實証文獻上的研究發現，卻有愈來愈多的証據支持此二個變數間的負向或無關係。為了解釋上述正向與負向間相反的矛盾關係，本篇論文嘗試利用兩種模型(非參數與非參數模型)與兩種效果(機會效果與動機效果)來解釋此二變數間的關係，此亦是本論文主要貢獻。其中機會效果是用以解釋失業率與犯罪間的負向關係，動機效果則用以解釋正向關係。在非參數模型中，利用失業率為景氣循環的代理變數，發現失業率與竊盜間存在正向關係，此與大多實証研究相符；失業率則和妨害風化與殺人犯罪間呈現負向相關；失業率與傷害罪間則沒有明顯正負關係。研究亦顯示，不同的犯罪類型在不同的參數模型下，統計的顯著性亦有不同，而在不同年齡層(青少年與成年人)的犯罪模型則更與理論模型結論相符。 / According to the theoretical literature on criminal economics, unemployment rate tends to be positively correlated to all types of crimes. However, more and more empirical evidence suggests otherwise. In order to clarify the relationship, this study exploits both nonparametric and parametric models and considers two effects, including opportunity and motivation effects. The presence of the opportunity effect leads to be a negative correlation between unemployment rate and crimes, while the presence of the motivation effect gives a positive correlation. Under nonparametric model where unemployment rate is used as a proxy for business cycles, we only found that there is positive correlation between unemployment rate and robbery, while obscenity and homicide are found to be negatively correlated with unemployment rate. This is in line with most empirical studies. Little correlation evidence is found for unemployment and other types of crimes. Under parametric model, the study indicates that the statistical significance differs in models, and depends on crime variable used. We found more consistent results with theoretic models for the age groups (teenagers and adults).

在製藥工業中，藥量特性之研究常被應用於藥理學、毒物學及臨床試驗中。藥量特性之研究同時在臨床試驗中的第一階段的藥物安全性及第二階段的藥物有效性中扮演著重要的角色。透過藥量特性的研究，使我們對於藥物的開發有著更深一層的認識，並可藉此縮短藥物核准上市的時間。 在多數的情況下，我們對於藥物動力學之參數與藥物劑量間的線性關係，有著特別的興趣。基於這個目的，一些典型的方法即是由一般線性模式發展而成的。然而，這些典型的統計方法常遇到下列的難題而違反其假設：（一）不同藥物劑量間的異質變異性。（二）不滿足常態性的假設。針對這些問題，我們藉由比較不同劑量間的斜率關係的無母數檢定程序來評估其線性關係並刻劃出藥物的反應曲線，文中並藉此方法舉出交叉實驗之實例。 / The problem of characterizing dose response curve for a pharmacokinetic parameter over a specific dose range is considered. In many cases, it is of interest to determine dose linearity (or dose proportionality) between the pharmacokinetic parameters and dose levels. For this purpose, several classical methods based on a general linear model procedure are available. However, two difficulties commonly encountered, namely (i) heterogeneity of the varibility at different dose levels and (ii) violation of the normality assumptions, often make the classical methods not applicable. To account for these problems, we propose a general nonparametric test procedure by comparing the slopes at different dose level to asses dose linearity and to characterize dose response curve. An example concerning the study of dose response of a compound based on a four-way crossover experiment is presented.

近年來剖面資料的監控在統計製程控制中有很大範圍的應用。在這篇論文裡，我們針對監控無母數剖面資料提出一個實務上的操作方法。這個操作方法有下列這些重要的特色：(1)使用一個靈活且有計算效率的無母數模型B-spline來描述反應變數與解釋變數的關係；(2)一般迴歸模型中之殘差結構假設是不需要的；(3)允許剖面資料內之觀測值間具有相關性之結構。最後，我們利用一個無線偵測器的實際資料來評估所提出方法的效率。 / Profile monitoring has received increasingly attention in a wide range of applications in statistical process control (SPC). In this work, we propose a practical proposed guide which has the following important features: (i) a flexible and computationally efficient smoothing technique, called the B-spline, is employed to describe the relationship between the response variable and the explanatory variable(s); (ii) the usual structural assumptions on the residuals are not require; and (iii) the dependence structure for the within-profile observations is appropriately accommodated. Finally, a real data set from a wireless sensor is used to evaluate the efficiency of our proposed method.