處理缺失之資料，已經有一些插補方法，但這些插補方法在不同情況下是否確實有效，仍有待探討pd Van Buuren et al.(2006) 對兩種不相容性模型 (一條件分配函數為線性，另一條件分配函數分別為平方及對數)進行討論，該論文依據模擬結果，僅表示在此兩不相容性模型下的插補方法似乎仍有效。本文則不僅嘗試解釋此兩模型為何有效，且進一步探討是否所有的不相容性模型插補後能與母體參數值相似而達到有效插補，並檢定其模擬後之結果，本文發現其答案為否定。 / There are some available imputation methods to deal with missing data. However, whether imputation methods based on conditional distributions are effective is still questionable. Van Buuren et al.(2006) discuss two incompatible conditional distributions models (one conditional distribution has a linear relation, the other conditional distribution has a squared or a logarithmic relation). According to their simulation results, Van Buuren et al.(2006) conclude that imputation methods based on these two incompatible models are effective. In this thesis, we try to explain why the two imputation models are effective. In addition, we discuss whether all imputation methods based on incompatible models give estimated parameter values close to the true values. The simulation results of these methods are also tested statistically to answer this question. In conclusion, we find the answer is negative.

No description available.

關於二維之變數，Arnold and Press (1989) 首先提出檢驗兩個條件分配是否滿足相容性的理論。本研究嘗試對n維之變數，探討n個條件分配滿足相容性的檢驗方式；並提出在三維聯合分配下，給定三個條件分配為常態(normal) 時，檢驗此三個條件分配滿足相容性的充分必要條件；最後，並推導出此三個條件分配滿足相容性時，其所對應的聯合機率密度函數之公式。若此三個條件分配其所對應的聯合機率密度函數進一步假設為常態時，檢驗其相容性的充分必要條件可更加以簡化。 / Arnold and Press (1989) first provide the theory about the compatibility of two conditional distributions in two dimensions. In this research, we extend the two dimensional cases to the high dimensional cases. In particular, we find the necessary and sufficient conditions of the compatibility of three conditional normal distributions in three dimensions. Furthermore, we also provide a formula to find the joint probability density function when three dimensional conditional normal distributions are compatible. Finally, simple sufficient and necessary conditions are also given when the joint distribution is further assumed to be normal.

根據Arnold and Press (1989) 提出檢驗兩個條件分配是否滿足相容條件的理論內容，本研究推論出，當給定二個條件機率密度函數的形式為常態（normal）時，如何判斷這兩個條件常態分配是否相容的充要條件，並進而推論出這兩個條件常態分配對應的聯合機率密度函數亦為常態分配的條件。我們更進一步透過電腦模擬方法，提供兩個不同聯合常態分配下所分別得到的兩組不同條件分配樣本，據以推得當對應的母數相差到何種程度時，可判定這兩組樣本其原始母體不同。 / Arnold and Press (1989) provide the theory about the compatibility of two conditional densities. In this research, we use their results to find the sufficient conditions of the compatibility of two conditional densities, which have the normal form. New sufficient conditions are also given if we further assume that corresponding joint density is normal. In addition, we use computer to generate two different samples from two different conditional normal distributions, which are from two different joint normal distributions. With the repeated samples, we provide the ranges of one population parameter when the other population parameters are fixed so that the samples are almost always incompatible.

電子產品及通訊產品具有相容性與網路外部性的產品特性，本文探討電信產業中，通訊產品與服務所特有的「網路外部性」以及「產品相容性」之間的關係，文中利用兩階段的雙占Hotelling模型，說明相容性與網內外費率之間的關係，而產品相容性問題導致電信業者的網內外費率有所不同，形成的網路外部性也各不相同，廠商如何利用此一特性進行訂價與競爭，並分析不同的技術、成本的廠商訂價，與相容程度大小的決策。本研究顯示廠商擁有較高的技術時，將會使相容性提高，使網內外費率的差距減少，所產生的網路外部性也越高，相較於對手廠商，產生更高的利潤並且產生較高的消費者剩餘。若消費者對於品牌有不同的偏好，廠商將會減少網路的相容性以提高利潤。最後並解釋廠商之間若有勾結之情形，將會依據消費者的願付價格來訂價，且社會總福利將會較雙占競爭高，雙占競爭時廠商因為提供了過高的相容性而損失了效率。

給定兩個條件機率分配，判斷他們是否相容？是否有唯一的聯合機率分配？以及相容時，如何找出所有可能的聯合機率分配？是研究相容性相當重要的課題。本文針對有限離散型二維條件機率分配，以Arnold and Press(1989) 最先提出的比值矩陣法，及由Song , Li, Chen, Jiang, and Kuo (2010) 所提出的檢驗法為架構，提出新演算法且利用此演算法來設計程式，使程式能判斷兩條件機率分配是否相容，以及相容後可求出對應的所有聯合機率分配。本文亦依據新演算法並應用MATLAB軟體設計程式，讓使用者可以很快地對上述三個問題得到答案。 / When two conditional distributions are given, the following three important questions are likely to be raised. Are they compatible? Is the corresponding joint distribution unique if they are compatible? How do you find all the corresponding joint distributions if they are compatible? In this thesis, basing on ratio matrix method given first by Arnold and Press (1989), and on the method for checking compatibility existence, for checking uniqueness, and for finding all possible joint distributions provided by Song, Li, Chen, Jiang, and Kuo (2010), we provide a new algorithm to answer these questions. Using this new algorithm, we also provide a MATLAB computer program so that any user could get the answer quickly for the above three questions.

單變量c-特徵函數已被證明可處理一些難以使用傳統特徵函數解決的問題， 在本文中，我們首先提出其反演公式，透過此反演公式，我們獲得（1）Dirichlet隨機向量之線性組合的機率密度函數；（2）以一些有趣測度為參數之Ferguson-Dirichlet過程其隨機動差的機率密度函數；（3）Ferguson-Dirichlet過程之隨機泛函的Lebesgue積分表示式。 本文給予對稱分配之多變量c-特徵函數的新性質，透過這些性質，我們證明在任何$n$維球面上之Ferguson-Dirichlet過程其隨機均值是一對稱分配，並且我們亦獲得其確切的機率密度函數，此外，我們將這些結果推廣至任何n維橢球面上。 我們亦探討條件分配相容性的問題，這個問題在機率理論與貝式計算上有其重要性，我們提出其充要條件。當給定相容的條件分配時，我們不但解決相關聯合分配唯一性的問題，而且也提供方法去獲得所有可能的相關聯合分配，我們亦給予檢驗相容性、唯一性及建構機率密度函數的演算法。 透過相容性的相關理論，我們提出完整且清楚地統合性貝氏反演公式理論，並建構可應用於一般測度空間的廣義貝氏反演公式。此外，我們使用廣義貝氏反演公式提供一個配適機率密度函數的演算法，此演算法沒有疊代演算法（如Gibbs取樣法）的收斂問題。 / The univariate c-characteristic function has been shown to be important in cases that are hard to manage using the traditional characteristic function. In this thesis, we first give its inversion formulas. We then use them to obtain (1) the probability density functions (PDFs) of a linear combination of the components of a Dirichlet random vector; (2) the PDFs of random functionals of a Ferguson-Dirichlet process with some interesting parameter measures; (3) a Lebesgue integral expression of any random functional of the Ferguson-Dirichlet process. New properties of the multivariate c-characteristic function with a spherical distribution are given in this thesis. With them, we show that the random mean of a Ferguson-Dirichlet process over a spherical surface in n dimensions has a spherical distribution on the n-dimensional ball. Moreover, we derive its exact PDF. Furthermore, we generalize this result to any ellipsoidal surface in n-space. We also study the issue of compatibility for specified conditional distributions. This issue is important in probability theory and Bayesian computations. Several necessary and sufficient conditions for the compatibility are provided. We also address the problem of uniqueness of the associated joint distribution when the given conditionals are compatible. In addition, we provide a method to obtain all possible joint distributions that have the given compatible conditionals. Algorithms for checking the compatibility and the uniqueness, and for constructing all associated densities are also given. Through the related compatibility theorems, we provide a fully and cleanly unified theory of inverse Bayes formula (IBF) and construct a generalized IBF (GIBF) that is applicable in the more general measurable space. In addition, using the GIBF, we provide a marginal density fitting algorithm, which avoids the problems of convergence in iterative algorithm such as the Gibbs sampler.

給定兩個有限離散型條件分配，我們可以去探討有關相容性及唯一性的問題。Tian et al.(2009)提出一個統合的方法，將相容性的問題轉換成具限制條件的線性方程系統(以邊際機率為未知數)，並藉由 l_2-距離測量解之誤差，進而求出最佳解來。他們也提出了電腦數值計算法在檢驗相容性及唯一性時的準則。 由於 Tian et al.(2009)的方法是把邊際機率和為 1 的條件放置在線性方程系統中，從理論的觀點來看，我們認為該條件在此種做法下未必會滿足。因此，本文中將邊際機率和為 1 的條件從線性方程系統中抽離出來，放入限制條件中，再對修正後的問題求最佳解。 我們提出了兩個解決問題的方法：(一) LRG 法；(二) 干擾參數法。LRG 法是先不管機率值在 0 與 1 之間的限制，在邊際機率和為 1 的條件下，利用 Lagrange 乘數法導出解的公式，之後再利用 Rao-Ghangurde 法進行修正，使解滿足機率值在 0 與 1 之間的要求。干擾參數法是在 Lagrange 乘數法公式解中有關廣義逆矩陣的計算部份引進了微量干擾值，使近似的逆矩陣及解可快速求得。理論證明，引進干擾參數所增加的誤差不超過所選定的干擾值，易言之，由干擾參數法所求出的解幾近最佳解。故干擾參數法在處理相容性問題上，是非常實用、有效的方法。從進一步分析Lagrange 乘數法公式解的過程中，我們也發現了檢驗條件分配"理論"相容的充分條件。 最後，為了驗證 LRG 法與干擾參數法的可行性，我們利用 MATLAB 設計了程式來處理求解過程中的運算，並以 Tian et al.(2009)文中四個可涵蓋各種情況的範例來解釋說明處理的流程，同時將所獲得的結果和 Tian et al. 的結果做比較。 / Given two finite discrete conditional distributions, we could study the compatibility and uniqueness issues. Tian et al.(2009) proposed a unified method by converting the compatibility problem into a system of linear equations with constraints, in which marginal probability values are assumed unknown. It locates the optimum solution by means of the error of l_2 - discrepancy. They also provided criteria for determining the compatibility and uniqueness. Because the condition of sum of the marginal probability values being equal to one is in Tian et al.s’linear system, it might not be fulfilled by the optimum solution. By separating this condition from the linear system and adding into constraints, we would look for the optimum solution after modification. We propose two new methods: (1) LRG method and (2) Perturbation method. LRG method ignores the requirement of the probability values being between zero and one initially, it then uses the Lagrange multipliers method to derive the solution for a quadratic optimization problem subject to the sum of the marginal probability values being equal to 1. Afterward we use the Rao-Ghangurde method to modify the computed value to meet the requirement. The perturbation method introduces tiny perturbation parameter in finding the generalized inverse for the optimum solution obtained by the Lagrange multipliers method. It can be shown that the increased error is less than the perturbation value introduced. Thus it is a practical and effective method in dealing with compatibility issues. We also find some sufficient conditions for checking the compatibility of conditional distributions from further analysis on the solution given by Lagrange multipliers method. To show the feasibilities of LRG method and Perturbation method, we use MATLAB to device a program to conduct them. Several numerical examples raised by Tian et al.(2009) in their article are applied to illustrate our methods. Some comparisons with their method are also presented.

台北市自民國72年起，公佈實施土地使用分區管制規則以來，至今已十幾年，但對於住宅區之環境品質並無明顯改善，反而突顯實施土地使用分區之分組及允許使用組別的問題，究其原因，是法規制定太偏於混合使用及允許使用組別太多。尤其附條件允許組別更為嚴重，幾乎與商業區差不多，而其中產生一些行業別與住宅不相容的情形。 有鑑於此，本研究乃期望透過混合使用相關研究回顧遴選出適當之評估指標項目，再收集專家學者對評估指標之意見，進行修正所遴選之評估指標，作為混合使用環境品質之評估基礎。在其中發現混合使用評估指標相對權重以「守望相助與警衛」權重最大、其次是「購物方便性」、第三為「餐飲方便性」。而「垃圾收集」與「污水排放問題」之小指標相對權重較小。由此不難理解，在專家的觀念裡混合使用之居住環境需以居住安全性之「守望相助與警衛」為第一考量，然後才能考慮混合使用生活之便利性。 由以上所建構之評估指標，經收集居民的意見與專家之賦予權重之後，經整理計算後，所得到評估指數正負得知，混合使用環境品質評估指標中以「寧便居住環境」、「公共安全」之指數呈現正值，而「環境污染公害」為負值，將其大指標之指數加總，發現總值為正數，得知混合使用之居住環境可能是好處多於壞處。 得知評估指標之指數大小之後，筆者再建立相容性行業別操作方式，進行計算行業別之評估指數大小，並建立數學模式，發現行業別之指數總和越大，代表居民與專家愈能接受該行業。負面值越大表示排斥性越大。同時可理解相容性越高之行業對環境影響越少，且對生活機能幫助越大。進而可透過行業別之排序，依混合使用環境品質需求，再訂定不同混合標準，以塑造不同等級之居住環境。 另在新、舊地區之實證過程中得知；混合使用的行業會因道路寬度、區位而有不同混合比例，其中立體混合也與平面混合成正相關。而從實際新、舊地區之業種調查發現，在大安區之業種是屬於都市型，而在萬華區之業種是屬於鄰里型。 綜合言之；本研究透過相關理論回顧與分析，所建立住宅區土地混合使用之評估指標，作為相容性之行業別判斷依據。在其中發現行業別之相容性，可依本研究所擬之評估指標判斷業別對居住環境的影響情形，同時可透指數分析再訂定業種相容性標準，而進行衡量評估指標與行業別之相關性計算。尤其在行業別設立時，將可能對住宅使用產生正面或負面影響情形，以指標的方式表達；如行業別是否產生噪音振動、垃圾處理方式、停車問題、空氣污染..等等問題，儘可能再設有評估標準。待相容性行業別執行一段時間後，依執行情形來修正評估標準，以利後續土地混合使用業種相容性之參考。 / Since the announcement and execution of the Zoning Act of Taipei Metropolitan in 1983, there is no obvious improvement on the living quality in the residential areas. Conversely, there are some issues on the usage classification and permitted usage categories. After further research, it’s found that the Zoning Act biased on the mixed-use, which permitted too much usage in one category. The most serious one was the permitted usage in its appendix, which made the usage of residential area almost the same as the commercial area. After researching on the related documents on mixed-use, the study emerged the appropriate evaluation indicators. Then collecting the experts’ comments, the study modified evaluation indicators accordingly, which formed the bases of environmental evaluation of mixed-use. In between, the relative importance of top three indicators was ranked as “residents’ mutual help and guard”, “shopping convenience” and “dinning convenience”. Both “trash collection” and “waste water manipulation” were less concerned. It understandable that in experts’ concepts, the residential safety was the first consideration then the living convenience. Based on the above evaluation indicators and collected comments from the residents and experts, the study came out the positive and negative values of evaluation indicators. The “quiescence and convenience of living environment” and “public safety” were positive value but “environmental pollution” was negative value. Summing up the big indicators, the value was positive which meant people possibly evaluated highly on the mixed-use in the residential environment. Understanding the importance of indicators, the study rebuilt the operation model for compatible businesses, which calculated the values of business evaluation indicators and built mathematical model. Then the study found out that the greater positive values of summed up indicators, the more representative residents and experts accepted the business. The greater the negative value, the more exclusivity represented. More compatible businesses would less impact the environment but enhance the living functionality. Ranking the business sequences according to the needs of environmental quality in mixed-use, we could build up different grades of living environments by setting up different mixed-use standards. It was proven from the study on the new and old residential areas that the mixed-use ratio of businesses would be differed by the width of road and location in which vertical and horizontal mixed-use are positively related. From the field study, the businesses in Ta-An district belonged to the metropolitan type but those in Wan-Hua district belonged to the tithing type. In summary, the study went through the review and analysis of related thesis then built the evaluation indicators for mixed-use in residential area, which in turn were the bases to identify the businesses compatibility. Utilizing the evaluation indicators, we could identify the business compatibility and its impact on the living environment. Simultaneously, through indicator analysis, new business compatibility could be redefined and evaluate the relationship between evaluation indicators and business relativity. Especially for the business category, which would heavily impact the environment, the indicators could be identified as, e.g., voice and vibration pollution, trash manipulation, parking issue, air pollution...which needed more evaluation standards. After some time of execution, the results could be used to modify the evaluation standard, which would be the reference for the succeeding study of land mixed-use.

本文考慮當資訊不對稱下的逆向選擇問題存在時,如何遵循Myerson(1979)提出的揭露原則 (the revelation principle)來設計一套具備誘因相容性 (incentive compatibility)的存款保險契約,契約中的自有資本比率為要保機構的自我選擇變數 (self-selection variable),而保險費則為存保公司用來控制要保機構決策行為的控制變數(control var iable),依此可以建立一套自我選擇機能(self-selection mechanism),來促使要保機構誠實揭其風險類型的私有訊息(private information),進而將要保機構依風險高低正確分類,徹底解決訊息不對稱下的逆向選擇問題。