Objective: The objective of the present study was to evaluate the performance of the monothermal caloric screening test in a large sample of patients. Design: A retrospective analysis of the medical records of 1002 consecutive patients who had undergone vestibular assessment at the Mayo Clinic during the years 1989 and 1990 was conducted. Patients with incomplete alternate binaural bithermal (ABB) caloric testing, congenital or periodic alternating nystagmus, or bilateral vestibular loss were excluded from the study. Clinical decision theory analyses (relative operating characteristic curves) were used to determine the accuracy with which the monothermal warm (MWST) and monothermal cool (MCST) caloric screening tests predicted the results of the ABB caloric test. Cumulative distributions were constructed as a function of the cutoff points for monothermal interear difference (IED) to select the cutoff point associated with any combination of true-positive and false-positive rates. Results: Both MWST and MCST performed well above chance level. The test performance for the MWST was significantly better than that of the MCST for three of the four ABB gold standards. A 10% IED cutoff point for the MWST yielded a false-negative rate of either 1% (UW ≥25%) or 3% (UW ≥20%). The use of a 10% IED (UW ≥25%) for the MWST would have resulted in a 40% reduction (N = 294) in the number of ABB caloric tests performed on patients without a unilateral weakness. Conclusions: The results of this study indicated that the MWST decreases test time without sacrificing the sensitivity of the ABB caloric test.

國際間的互動頻繁，使得國家間的交往成為國家政策目標之一。因此 身為國際社會成員的我國，自不能孤立於國際社會而存在。我國由於國情 特殊，尤其是面對中共的刻意打壓與封鎖，因此對於參與國際社會，宣示 自己為國際社會的成員，一向是我國外交政策的重點所在。為突破外交孤 立的困境，「務實外交」政策便因應而生了！但是中共不願意我國在外交 與國際交往上有所突破，因此對我國之抨擊、打壓與封殺實乃愈加強烈。 在國際交往工具的選擇上，我國由於此種國際環境使然，因此很難運用一 般在正常情形下所使用的外交政策工具。因此「對外援助」政策便成為我 國拓展對外關係的主要政策工具之一。因為不僅可以運用發展與人道等特 質以避開敏感的政治限制，以達到國際交往的實質目的；再者，由於我國 經濟等方面之發展經驗實為其他開發中國家發展之楷模；亦符合「己立立 人，己達達人」之固有明訓。故正當我國擁有適當的經濟力量以作為推行 對外援助的籌 碼，而國際社會又正逢需求之際，因此便可以以此種較為 積極並較具影響力的方式進行國際交往。再者，它亦是我國參與國際事務 、善盡國際責任、提升國際形象與增加國際影響力的 表現。 我國 的對外援助政策始於民國四十七年七月，應越南政府之邀，組派經濟考察 團至越南考察。隔年，我國駐越技術團成立，為我國農技援外之始。民國 七十七年十月成立的「海外經濟合作發展基金」（ International Economic Cooperation Development Fund,IECDF）並在經濟部下設立基 金管理委員會開展基金業務，展開對外援助事宜。民國八十五年七月一日 ，財團法人「國際合作發展基金會」成立，整合及統籌我國對外援助事宜 。以使我國的對外援助工作能達到透明化、專業化與效率化。並量力而行 ，認清自己的力量。未來的工作方 向則包括雙邊或多邊技術合作、直 接或間接貸款、直接或間接參與投資、投資或貸款之保證與捐款或實物贈 與、以及其它可行方式。而合作對象則是外國政府、國際組織或國際機構 或其指定的機關或團體。以達我國回饋國際社會、善盡國際責任、重返國 際社會等目的。

Traditional multiple hypothesis testing procedures, such as that of Benjamini and Hochberg, fix an error rate and determine the corresponding rejection region. In 2002 Storey proposed a fixed rejection region procedure and showed numerically that it can gain more power than the fixed error rate procedure of Benjamini and Hochberg while controlling the same false discovery rate (FDR). In this thesis it is proved that when the number of alternatives is small compared to the total number of hypotheses, Storeys method can be less powerful than that of Benjamini and Hochberg. Moreover, the two procedures are compared by setting them to produce the same FDR. The difference in power between Storeys procedure and that of Benjamini and Hochberg is near zero when the distance between the null and alternative distributions is large, but Benjamini and Hochbergs procedure becomes more powerful as the distance decreases. It is shown that modifying the Benjamini and Hochberg procedure to incorporate an estimate of the proportion of true null hypotheses as proposed by Black gives a procedure with superior power.<p> Multiple hypothesis testing can also be applied to regression diagnostics. In this thesis, a Bayesian method is proposed to test multiple hypotheses, of which the i-th null and alternative hypotheses are that the i-th observation is not an outlier versus it is, for i=1,...,m. In the proposed Bayesian model, it is assumed that outliers have a mean shift, where the proportion of outliers and the mean shift respectively follow a Beta prior distribution and a normal prior distribution. It is proved in the thesis that for the proposed model, when there exists more than one outlier, the marginal distributions of the deletion residual of the i-th observation under both null and alternative hypotheses are doubly noncentral t distributions. The outlyingness of the i-th observation is measured by the marginal posterior probability that the i-th observation is an outlier given its deletion residual. An importance sampling method is proposed to calculate this probability. This method requires the computation of the density of the doubly noncentral F distribution and this is approximated using Patnaiks approximation. An algorithm is proposed in this thesis to examine the accuracy of Patnaiks approximation. The comparison of this algorithms output with Patnaiks approximation shows that the latter can save massive computation time without losing much accuracy.<p> The proposed Bayesian multiple outlier identification procedure is applied to some simulated data sets. Various simulation and prior parameters are used to study the sensitivity of the posteriors to the priors. The area under the ROC curves (AUC) is calculated for each combination of parameters. A factorial design analysis on AUC is carried out by choosing various simulation and prior parameters as factors. The resulting AUC values are high for various selected parameters, indicating that the proposed method can identify the majority of outliers within tolerable errors. The results of the factorial design show that the priors do not have much effect on the marginal posterior probability as long as the sample size is not too small.<p> In this thesis, the proposed Bayesian procedure is also applied to a real data set obtained by Kanduc et al. in 2008. The proteomes of thirty viruses examined by Kanduc et al. are found to share a high number of pentapeptide overlaps to the human proteome. In a linear regression analysis of the level of viral overlaps to the human proteome and the length of viral proteome, it is reported by Kanduc et al. that among the thirty viruses, human T-lymphotropic virus 1, Rubella virus, and hepatitis C virus, present relatively higher levels of overlaps with the human proteome than the predicted level of overlaps. The results obtained using the proposed procedure indicate that the four viruses with extremely large sizes (Human herpesvirus 4, Human herpesvirus 6, Variola virus, and Human herpesvirus 5) are more likely to be the outliers than the three reported viruses. The results with thefour extreme viruses deleted confirm the claim of Kanduc et al.

Traditional multiple hypothesis testing procedures, such as that of Benjamini and Hochberg, fix an error rate and determine the corresponding rejection region. In 2002 Storey proposed a fixed rejection region procedure and showed numerically that it can gain more power than the fixed error rate procedure of Benjamini and Hochberg while controlling the same false discovery rate (FDR). In this thesis it is proved that when the number of alternatives is small compared to the total number of hypotheses, Storeys method can be less powerful than that of Benjamini and Hochberg. Moreover, the two procedures are compared by setting them to produce the same FDR. The difference in power between Storeys procedure and that of Benjamini and Hochberg is near zero when the distance between the null and alternative distributions is large, but Benjamini and Hochbergs procedure becomes more powerful as the distance decreases. It is shown that modifying the Benjamini and Hochberg procedure to incorporate an estimate of the proportion of true null hypotheses as proposed by Black gives a procedure with superior power.<p> Multiple hypothesis testing can also be applied to regression diagnostics. In this thesis, a Bayesian method is proposed to test multiple hypotheses, of which the i-th null and alternative hypotheses are that the i-th observation is not an outlier versus it is, for i=1,...,m. In the proposed Bayesian model, it is assumed that outliers have a mean shift, where the proportion of outliers and the mean shift respectively follow a Beta prior distribution and a normal prior distribution. It is proved in the thesis that for the proposed model, when there exists more than one outlier, the marginal distributions of the deletion residual of the i-th observation under both null and alternative hypotheses are doubly noncentral t distributions. The outlyingness of the i-th observation is measured by the marginal posterior probability that the i-th observation is an outlier given its deletion residual. An importance sampling method is proposed to calculate this probability. This method requires the computation of the density of the doubly noncentral F distribution and this is approximated using Patnaiks approximation. An algorithm is proposed in this thesis to examine the accuracy of Patnaiks approximation. The comparison of this algorithms output with Patnaiks approximation shows that the latter can save massive computation time without losing much accuracy.<p> The proposed Bayesian multiple outlier identification procedure is applied to some simulated data sets. Various simulation and prior parameters are used to study the sensitivity of the posteriors to the priors. The area under the ROC curves (AUC) is calculated for each combination of parameters. A factorial design analysis on AUC is carried out by choosing various simulation and prior parameters as factors. The resulting AUC values are high for various selected parameters, indicating that the proposed method can identify the majority of outliers within tolerable errors. The results of the factorial design show that the priors do not have much effect on the marginal posterior probability as long as the sample size is not too small.<p> In this thesis, the proposed Bayesian procedure is also applied to a real data set obtained by Kanduc et al. in 2008. The proteomes of thirty viruses examined by Kanduc et al. are found to share a high number of pentapeptide overlaps to the human proteome. In a linear regression analysis of the level of viral overlaps to the human proteome and the length of viral proteome, it is reported by Kanduc et al. that among the thirty viruses, human T-lymphotropic virus 1, Rubella virus, and hepatitis C virus, present relatively higher levels of overlaps with the human proteome than the predicted level of overlaps. The results obtained using the proposed procedure indicate that the four viruses with extremely large sizes (Human herpesvirus 4, Human herpesvirus 6, Variola virus, and Human herpesvirus 5) are more likely to be the outliers than the three reported viruses. The results with thefour extreme viruses deleted confirm the claim of Kanduc et al.

In 1988, Owen introduced empirical likelihood as a nonparametric method for constructing confidence intervals and regions. Since then, empirical likelihood has been studied extensively in the literature due to its generality and effectiveness. It is well known that empirical likelihood has several attractive advantages comparing to its competitors such as bootstrap: determining the shape of confidence regions automatically using only the data; straightforwardly incorporating side information expressed through constraints; being Bartlett correctable. The main part of this thesis extends the empirical likelihood method to several interesting and important statistical inference situations. This thesis has four components. The first component (Chapter II) proposes a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve in order to overcome the computational difficulty when we have nonlinear constrains in the maximization problem. The second component (Chapter III and IV) proposes smoothed empirical likelihood methods to obtain interval estimation for the conditional Value-at-Risk with the volatility model being an ARCH/GARCH model and a nonparametric regression respectively, which have applications in financial risk management. The third component(Chapter V) derives the empirical likelihood for the intermediate quantiles, which plays an important role in the statistics of extremes. Finally, the fourth component (Chapter VI and VII) presents two additional results: in Chapter VI, we present an interesting result by showing that, when the third moment is infinity, we may prefer the Student's t-statistic to the sample mean standardized by the true standard deviation; in Chapter VII, we present a method for testing a subset of parameters for a given parametric model of stationary processes.

我國的信用卡市場在民國八十二年全面開放以來，發展至今不過10餘年，已成為全球成長最快速的信用卡市場之一。但近年來也隨著信用卡業務已有相當顯著的成長，然而信用卡不僅只是一種支付工具，也屬於免擔保的信用融資，對發卡銀行而言，風險很高。故本文對於銀行要如何快速且正確的掌握客戶信用與還款能力，以防範呆帳發生，也變得日趨重要。 故本文利用Binary Quantile Regression可用於探討解釋變數對於被解釋變數在給定「特定分位數之下的邊際效果」，提供不同分位數的估計結果，可用於觀察被解釋變數的整個分配狀況。在實證上，二元分量迴歸模型不只可用來解釋平均的狀況，更常用來觀察分配尾端的情況。在以ROC與CAP的信用風險模型來驗證其Binary Quantile Regression的效力。

本文主旨在分析構成撒哈拉以南的非洲國家決定中斷或抑制承認中華民國為主權國家原因。過去的幾十年來，中華民國的邦交國數目大幅下降，大部分位於撒哈拉沙漠以南的非洲國家都在其中。舉例來說，1964年是中華民國在非洲地區外交上的 峰期，台北獲得了22個國家的承認。然而，現今只剩下3個國家的承認。 這個研究計劃，企圖藉由關注研究撒哈拉沙漠以南的非洲國家不繼續承認台北的動機，使這種趨勢能更加被瞭解。這點是非常重要的，因為自1960年以來，中華民國已經將非洲視為在其謀求國際承認最有潛力的區域。而在這個層面，便不能輕忽中華人民共和國在其中所扮演的角色。驅使在“一個中國”的原則下，北京當局在推動提昇這些國家的整體國家利益上所擁有的能力，對中華民國在撒哈拉沙漠以南的非洲友邦國家而言，是推動他們轉向，開啟兩個中國外交競爭的一股重要力量。為了解釋這一種傾向，本文應用了新現實主義理論和其中的“bandwagon behaviour”模說明。 筆者預期本文能達到的目的包含了提供一個新的視角來看待中華民國與非洲的關係，用來評估非洲國家對於此問題所持有的立場。筆者希望能夠針對現今中華民國和非洲國家間脆弱的外交地位，帶來新的見解，並進一步提供關於非洲各國和中華民國之間關係的科學論證。 / This thesis aims to analyze the possible reasons shaping the sub-Saharan African states’ decisions in withdrawing or refraining from recognizing the Republic of China (ROC). In the last decades the number of the ROC’s diplomatic allies has decreased drastically and the majority of states located south of the Sahara Desert have taken part in this process. For instance, at the peak of its success in Africa in 1964, Taipei was recognized by twenty two countries. Yet, today it is only recognized by three states. The research conducted is an attempt to provide a better understanding of this trend by focusing on the sub-Saharan African states’ motivations in not extending recognition to Taipei. This is important because since the 1960s, Africa has become a potential area in the ROC’s quest for international recognition. In this regard, one should not disregard the role of the People’s Republic of China. Within the “one China” principle, Beijing’s capacity in advancing these states national interests has been an important driving force in diverting sub-Saharan countries’ allegiance from the ROC in the two China’s diplomatic competition. In order to explain this tendency, the Neo-realism theory and its “bandwagon” behavior will be applied. The expected contributions from this work include a new perspective on the ROC-Africa relations in which an evaluation of the African stance regarding this issue is proposed. The author hopes to bring new insights on the current vulnerable diplomatic position of the ROC in Africa, thus further contributing to the scientific debate on the relationships between African countries and the ROC.

In the field of diagnostic test studies, the accuracy of a diagnostic test is essential in evaluating the performance of the test. The receiver operating characteristic (ROC) curve and the area under the curve (AUC) are widely used in such evaluation procedures. Meanwhile, the Youden index is also introduced into practice to measure the accuracy of the diagnostic test from another aspect. The Youden index maximizes the sum of sensitivity and specificity, assuring decent true positive and negative rates. It draws one's attention due to its merit of finding the optimal cut-off points of biomarkers. Similar to Partial ROC, a new index, called "Partial Youden index" can be defined as an extension of Youden's Index. It is more meaningful than regular Youden index since the regular one is just a special case of the Partial Youden Index. In this thesis, we focus on construction of generalized confidence intervals for the Partial Youden Index and its corresponding optimal cut-off points. Extensive simulation studies are conducted to evaluate the finite sample performances of the new intervals.

Receiver operating characteristic (ROC) curves have been widely used in evaluation of the goodness of the diagnostic method in many study fields, such as disease diagnosis in medicine. The area under the ROC curve (AUC) naturally became one of the most used variables in gauging the goodness of the diagnosis (Mossman, Somoza 1991). Since medical diagnosis often is not dichotomous, the ROC curve and AUC need to be generalized to a multi-dimensional case. The generalization of AUC to multi-class case has been studied by many researchers in the past decade. Most recently, Nakas & Yiannoutsos (2004) considered the ordered d classes ROC analysis by only considering the sensitivities of each class. Hence, their dimension is only d. Cha (2005) considered more types of mis-classification in the ordered multiple-class case, but reduced the dimension of Ferri, at.el. from d(d-1) to 2(d-1). In this dissertation we are trying to adjust and calculate the VUS for an ordered multipleclass with Cha’s 2(d-1)-dimension method. Our methodology of finding the VUS is introduced. We present the method of adjusting and calculating VUS and their statistical inferences for the 2(d-1)-dimension. Some simulation results are included and a real example will be presented. Intellectual outcomes in pediatric brain-tumor patients were investigated in a prospective longitudinal study. The Standard-Binet Intelligence Scale-Fourth Edition (SB-IV) Standard Age Score (SAS) and Composite intelligence quotient (IQ) score are examined as cognitive outcomes in pediatric brain-tumor patients. Treatment factors, patient factors and time since diagnosis are taken into account as the risk factors. Hierarchical linear/quadratic models and Gompertz based hierarchical nonlinear growth models were applied to build linear and nonlinear longitudinal curves. We use PRESS and Volume Under the Surface (VUS) as the criterions to compare these two methods. Some model interpretations are presented in this dissertation.

The receiver operating characteristic (ROC) curves is a popular tool for evaluating continuous diagnostic tests. The traditional definition of ROC curves incorporates implicitly the idea of "hard" thresholding, which also results in the empirical curves being step functions. The first topic is to introduce a novel definition of soft ROC curves, which incorporates the idea of "soft" thresholding. The softness of a soft ROC curve is controlled by a regularization parameter that can be selected suitably by a cross-validation procedure. A byproduct of the soft ROC curves is that the corresponding empirical curves are smooth. The second topic is on combination of several diagnostic tests to achieve better diagnostic accuracy. We consider the optimal linear combination that maximizes the area under the receiver operating characteristic curve (AUC); the estimates of the combination's coefficients can be obtained via a non-parametric procedure. However, for estimating the AUC associated with the estimated coefficients, the apparent estimation by re-substitution is too optimistic. To adjust for the upward bias, several methods are proposed. Among them the cross-validation approach is especially advocated, and an approximated cross-validation is developed to reduce the computational cost. Furthermore, these proposed methods can be applied for variable selection to select important diagnostic tests. However, the above best-subset variable selection method is not practical when the number of diagnostic tests is large. The third topic is to further develop a LASSO-type procedure for variable selection. To solve the non-convex maximization problem in the proposed procedure, an efficient algorithm is developed based on soft ROC curves, difference convex programming, and coordinate descent algorithm.