The unimodality of a function seems a simple concept. But in the Euclidean space R^m, m=3,4,..., it is not easy to define. We have an easy tool to find the minimum point of a unimodal function. The goal of this project is to formalize and support distinctive strategies that typically guarantee convergence. Support is given both by analytic arguments and simulation study. Application is envisioned in low-dimensional but non-trivial problems. The convergence of the proposed iterated grid search algorithm is presented along with the results of particular application studies. It has been recognized that the derivative methods, such as the Newton-type method, are not entirely satisfactory, so a variety of other tools are being considered as alternatives. Many other tools have been rejected because of apparent manipulative difficulties. But in our current research, we focus on the simple algorithm and the guaranteed convergence for unimodal function to avoid the possible chaotic behavior of the function. Furthermore, in case the loss function to be optimized is not unimodal, we suggest a weaker condition: almost (noisy) unimodality, under which the iterated grid search finds an estimated optimum point. / Ph. D.

由於社會變遷迅速，文化資產保存工作，無論在有形或無形資產方面均面臨了嚴苛的挑戰。許多為保存歷史建物、遺址、文物或技藝之民間組織或政府文化機構無不極力爭取以獲得必要的經費資源，以防止文化資產的快速流逝。近年來政府對文化資源的投入程度受到廣泛關注，在財政緊縮下，政府削減各項支出中有關文化設施之補助，或限縮地方政府的文化預算，引起各界對文化預算資源配置問題的熱烈討論，導致以經濟觀點衡量文化產出或文化設施之評價日顯重要。在俱歷史性之藝術或文化資源領域，由於其價值無法快速藉由市場價格機制訂出來，衡量文化政策之最適資源投資一直引起激烈爭議，在各部會資源競爭之下，為了獲得足夠的預算分配，政府各部門必須彰顯其對整體經濟效益之貢獻，因此近年來越來越多研究針對非市場財貨之公共投資進行經濟效益評估。調查民眾對文化公共財的願付價格，除可顯示民眾對文化公共財偏好強度以進行成本效益分析外，亦可作為該文化機構自行籌措財源擬訂定價策略之參考，並可提供政府當局財政配置及公共投資之依據，本篇研究將以非市場財貨評估中之條件評估法，以文建會所屬文化機構國立傳統藝術中心為例，求算民眾對該機構之願付價格。 / 實證結果，在估計參數值部份，發現文化資產保存重要性認同度、文化資產遺贈價值認同度、文化資產預算擴編認同度、年齡、文化產業消費頻率等變數，對受訪者的支付意願均有顯著影響；第一階段與第二階段的詢價金額係數估計值為負並且顯著，表示當詢價金額提升時，受訪者會傾向於不願意支付。在單界二元選擇問答下，Logit模型估算其值為181.56元，Probit模型估算其值為199.12元，在95％信心水準下區間估計值Logit模型其值為191.56元到171.56元之間，Probit模型其值為205.90元到192.34元之間；在雙界二元選擇問答下以Bivariabe Probit 估算結果得到第一次詢價的願付價格為145.69元，第二次詢價的願付價格為218.42 元，實證結果單界與雙界二元選擇模型願付價格差異不大。 / Nowadays, historic building, monument, and artifacts, facing difficult issue of damaging, are quickly dying away. Agencies and organizations whose mission is to protect and preserve historic and culturally important building, monument, and artifacts from the ravages of weather, pollution, development, and even use by the general public must compete urgently for needed resources. Government funding of the cultural arts has received considerable attention in recent years. Efforts to cut funding to the national endowment for the culture and declining budgets for public cultural organizations and art institution have raised questions about how much individuals value the culture and arts. Measuring the economic value of particular arts policies or public cultural organizations is difficult and important. The hard case for measuring economic value of cultural resources is that they are not captured readily by market prices. The appropriate resources to be allocated in public cultural or art institutions often get heated and considerable debate. Valuing the willingness to pay for cultural public goods, not only can be applied for measuring economic value to be used in benefit-cost analysis of public project, but also more efficient in the selection of investment program if the total value（use value and non-use value）can be estimated. The purpose of this study is using one of the non-market goods valuation method, contingent valuation method, to elicit a willingness to pay from individual for hypothetical changes in some situation, further more to value the use value and non-use value of the“National Center for Traditional Art ”. / The variables such as the IMPO,BEQU, BUDG, AGE, FRE1, have a significant positive effect on the WTP for a cultural public good valuing. The table broadly indicates that as the bid level is increased, the number of willing to pay the amount decreased. The empirical results show that under the single-bounded dichotomous choice model, the estimated WTP for Logit model is NT$181.56 and for Probit model is NT$199.12. Under the 95％ confidence, for Logit mode the estimated WTP is between NT $191.56 and NT $171.56, and for Probit model is between NT $205.90 and NT $192.34. Under the double-bounded dichotomous choice model, Bivariate Probit model was adopted to estimate the WTP. The first-estimated WTP is NT $145.69, and second-estimated WTP is NT $218.42. The estimated WTP under double bounded dichotomous choice model is not much different from the estimated WTP under single bounded dichotomous choice model.

我們提供一個新的可靠度模型，DwACM，並提供一個模式選擇準則CCP，我們利用DwACM和CCP來選擇衰變量。 / We propose a new reliability model, DwACM (Dichotomous-data with Auxiliary Continuous Measurements model) to describe a data set which consists of classical dichotomous response (Go or No Go) associated with a set of continuous auxiliary measurement. In this model, the lifetime of each individual is considered as a latent variable. Given the value of the latent variable, the dichotomous response is either 0 or 1 depending on if it fails or not at the measuring time. The continuous measurement can be regarded as observations of an underlying possible degradation candidate of which descending process is a function of the lifetime. Under the assumption that the failure of products is defined as the time at which the continuous measurement reaches a threshold, these two measurements can be linked in the proposed model. Statistical inference under this model are both in frequentist and Bayesian frameworks. To evaluate the continuous measurements, we provide a criterion, CCP (correct classification probability), to select the best degradation measurement. We also report our simulation studies of the performances of parameters estimators and CCP.

Particulate matter in the ambient air of down-town New Orleans, LA, is not currently recorded by any government, state, or private organization. This research quantified particulate matter (PM) and its metal concentration in ambient air of the New Orleans Historic District. Both, PM10 (PM less than 10 micron in size) and PM2.5 (PM less than 2.5 micron in size) were quantified by gravimetric analysis using an Andersen Dichotomous Sampler (Series 240). Posterior to gravimetric analysis, the filters were analyzed with a fluorescent test method using an Innov-X Portable XRF Analyzer (Model A-6500). This study demonstrated that the ambient air of the New Orleans Historic District is in compliance with the National Ambient Ai Quality Standards regarding contamination of particulate matter and Lead.

假設市場評價法（Contingent valuation）多用於評估有關某一非市場性財產（Non-market goods）或公共財（Public goods）在民眾心目中的願付價值（Willingness to pay, WTP）。探討受訪者願付價值之研究調查案的問卷設計方式，大致可分成五種，其中開放式出價法和逐步競價法已被證實會對估計造成偏誤，而支付卡法、二分選擇法和雙界二分選擇法則是現今較常為研究者所使用的價格詢問方法，本論文的研究是針對二分選擇法的最佳設計（Optimal design），作一深入的探討。 假設欲探究之母體的願付價值為一服從平均數為 、標準差為 的常態分配，若採用二分選擇法作為價格詢問的方式，則何種詢問方法才能讓參數估計最佳化，由模擬實驗的結果，我們知道若將受訪者隨機等分成兩群，分別詢問兩個不同的價格，且這兩個價格的平均等於預先猜測的母體平均數，那麼不但會有相當不錯的估計結果，在實際的執行上亦較方便。此外，我們提出較容易計算的參數估計量來代替傳統的最大概似估計量（MLE），並以數理證明保證了新的參數估計量有良好的估計性質。 願付價值的研究若對母體資訊不充分時，常會先採行前測（Pretest）。本論文除了探討二分選擇法的最佳設計之外，亦針對支付卡法和二分選擇法運用在前測時，作一深入的討論，結果發現當事先猜測的母體分配參數和真實分配相差很多下，支付卡法和二分選擇法會產生無法估計的情況，因此我們提出新的前測方法，試圖彌補這兩種傳統前測法的不足，我們稱之為序列詢問法（Sequence method）。序列詢問法為一種追蹤母體平均數的方式，依照現在這位受訪者的回答，決定下一位受訪者的詢問價格，在我們的研究中發現，如此的序列詢問方法比傳統的前測法利用更少的資訊，但仍然維持不錯的母體平均數估計結果。

本文應用環境經濟學上非市場環境財估價方法－－假設市場評價法，評估北部地區四條河川（淡水河、基隆河、新店溪與大漢溪）在水質或景觀的整治時，北部地區居每人每年的願付價值，本文的目的是提供河川整治環境改善效益面的訊息，以利政府不管是作事前或事後的評估，皆可利用本研究結果的經濟效益資料作成本效益分析，以為河川整治之公共政策施政的參考與政策評估。由於，本文研究結果包括四條河川的水質與景觀在各種改善目標下之願付價值，所以，透過成本效益分析，政府在財政收支日益吃緊的情況下，可以知道在預算限制下應先整治哪一條河川可達最大經濟效益，且各河川條件不同，故整治目標的訂定亦有不同，本研究結果方可提供政府河川之環境改善目標訂定的參考依據。 　　在假設市場評價法中詢價方式有逐步競價法、支付卡、開放式問卷、封閉式問卷與假設市場序列法，本研究的問卷實驗設計採封閉式問卷中的雙界二分選擇法，實證模型採存活模型中的比例尺度模型作迴歸分析，推估受訪者在各河川、各種環境品質改善標的下的願付價值。 　　在迴歸分析中，得知影響受訪者願付價值的主要因素是，一在受訪者的特性變數中，教育程度、過去一年的戶外旅遊次數、家中汽車數與年家庭所得等變數對願付價值是正向顯著影響，而性別與年齡兩變數則是負相關。另一在環境品質變數中，景觀改善等級變數對願付價值是正向顯著影響，然而在水質改善的環境變數中，不論是目前的水質等級或是水質改善到各種不同乾淨程度的變數，都對受訪者頗付價值的影響不甚顯著。本文同時針對四條河川包括已進行整治的淡水河與基隆河，以及尚未進行整治工程的新店溪與大漢溪作環境改善效益評估，是與過去文獻主要差異之處。

This thesis examines 5-year clinical and health-economic outcomes of ischaemic stroke, and their relationship to short-term post-stroke disability, as captured by the 3-month modified Rankin Scale (mRS) - the favoured primary outcome measure in acute stroke trials. I use data from the Oxford Vascular Study (recruited 2002-2014), a population-based prospective cohort for which I followed patients in-person and via medical records until 15-May-2017. I demonstrate that 3-month mRS strongly predicts 5-year post-stroke disability and mortality, including in clinically-relevant groups (treatable major strokes, atrial fibrillation-related strokes, and lacunar strokes), reaffirming its use as a trial outcome measure. About one in four patients experience functional recovery between 3-12 months post-stroke, and mortality follow-up beyond 1-year by stroke trials can show translation of early disability gains into lower mortality. Contrary to previously reported apparent sex-differences, I find no evidence of worse outcomes in women after accounting for differences in age and pre-stroke mRS. I find that late recovery between 3-12 months occurs more often in lacunar strokes, supporting the focus of restorative therapies in this group, but highlighting that uncontrolled studies cannot assume that improvements after 3-months are treatment-related. In addition, I demonstrate that like death/disability, outcomes of institutionalization, post-stroke dementia, health/social-care costs, and quality-adjusted life expectancy (QALE) also show meaningful differences with each step up the mRS ladder. Consequently, ordinal analysis of the 3-month mRS (capturing transitions across the scale's range) better predicts long-term outcomes than dichotomous approaches, which also foster high exclusion rates of relevant patient segments from trials owing to their pre-morbid disability. However, the mRS should be weighted in ordinal analyses, as different state transitions carry different implications for long-term outcomes. Using 3-month mRS-stratified data for clinical endpoints, care costs, and QALE, I derive mRS weights that could be used for meaningful ordinal analyses, clinical prognostication, and cost-effectiveness analyses of stroke therapies.

L‟objectif de toute analyse économique sur l‟offre de travail, est en général, de mieux cerner les problématiques liées à l‟emploi permettant de décliner des politiques en direction du marché du travail. Cette thèse n‟échappe pas à cet objectif bien qu‟elle soit orientée vers les femmes. A partir des analyses développées dans cette thèse, nous avons apporté un nouvel éclairage sur les facteurs déterminants qui poussent ou empêchent la femme sénégalaise à intégrer le marché du travail. Les approches théoriques développées, nous ont conduit à considérer la nature des relations conjugales, les différentes perceptions du travail et des obligations familiales correspondants à différents types de comportements féminins d‟offre de travail. Le comportement d‟offre de travail de la femme sénégalaise est ainsi influencé par des caractéristiques individuelles telles que l‟âge, le niveau d‟éducation, et des caractéristiques familiales courantes telles que la présence d‟enfant(s) de moins de 5ans dans le ménage, la présence d‟un conjoint (statut matrimonial), le revenu du conjoint, la taille du ménage, le statut monétaire matérialisé par la pauvreté, le versement de transferts à des descendants ou ascendants.Par le biais de la modélisation logistique dichotomique et multinomiale, nous avons montré que le niveau d‟éducation est positivement corrélé à la participation des femmes sur le marché du travail et constitue de surcroît, un ticket d‟entrée dans le secteur public. Contrairement au statut matrimonial (être mariée), la présence d‟enfants de moins de 5 ans et le revenu du conjoint ne semblent pas être un obstacle à l‟intégration des femmes sur le marché du travail, mais cette présence d‟enfant semble orienter les sénégalaises vers le secteur informel au détriment des autres secteurs (public et privé formel). Ce qui est souvent motivé par les conditions de travail plus flexibles dans ce secteur permettant aux femmes de concilier activités économiques et obligations familiales. Par ailleurs, les femmes appartenant aux ménages pauvres semblent être plus disposer à offrir du travail que celles appartenant aux ménages non pauvres, mais elles ont moins de chances d‟être dans le secteur public, le secteur privé formel et dans une moindre mesure dans les ambassades et ONG que dans l‟informel par rapport à celles qui ne sont pas pauvres. / The objective of any economic analysis of the elabor supply is generally to better understand issues related to employment allowing formulating policies towards the labor market. This thesis is not an exception to this objective although it focuses exclusively on women. From the analysis of the present thesis, we have shed new light on the main factors driving or inhibiting the senegalese woman to enter the labor market. The theoretical approaches developed have led us to consider the nature of marital relationships, the different perceptions of work and family obligations corresponding to different types of female behavior of labor supply. Through a dicotomous and multinomial logit model, we have shown that the behavior of labor supply of senegalese women is influenced by individual characteristics such as the age and education level, and standard family characteristics such as the presence of under 5 years old child/children in the household, the presence of a spouce (marital status), the income of the spouse, the householf size, the monetary status indicated by the poverty, the remittances to descendants or ascendants.

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