本文主要在探討自變數存在有測量誤差時，邏輯式迴歸模型的估計問題，並設計實驗使得測量誤差能滿足遞減假設，進一步應用序貫分析方法，在給定水準下，建立一個信賴範圍。 當自變數存在有測量誤差時，通常會得到有偏誤的估計量，進而在做決策時會得到與無測量誤差所做出的決策不同。在本文中提出了一個遞減的測量誤差，使得滿足這樣的假設，可以證明估計量的強收斂，並證明與無測量誤差所得到的估計量相同的近似分配。相較於先前的假設，特別是證明大樣本的性質，新增加的樣本會有更小的測量誤差是更加合理的假設。我們同時設計了一個實驗來滿足所提出遞減誤差的條件，並利用序貫設計得到一個更省時也節省成本的處理方法。 一般的case-control實驗，自變數也會出現測量誤差，我們也證明了斜率估計量的強收斂與近似分配的性質，並提出一個二階段抽樣方法，計算出所需的樣本數及建立信賴區間。 / In this thesis, we focus on the estimate of unknown parameters, experimental designs and sequential methods in both prospective and retrospective logistic regression models when there are covariates measured with errors. The imprecise measurement of exposure happens very often in practice, for example, in retrospective epidemiology studies, that may due to either the difficulty or the cost of measuring. It is known that the imprecisely measured variables can result in biased coefficients estimation in a regression model and therefore, it may lead to an incorrect inference. Thus, it is an important issue if the effects of the variables are of primary interest. When considering a prospective logistic regression model, we derive asymptotic results for the estimators of the regression parameters when there are mismeasured covariates. If the measurement error satisfies certain assumptions, we show that the estimators follow the normal distribution with zero mean, asymptotically unbiased and asymptotically normally distributed. Contrary to the traditional assumption on measurement error, which is mainly used for proving large sample properties, we assume that the measurement error decays gradually at a certain rate as there is a new observation added to the model. This kind of assumption can be fulfilled when the usual replicate observation method is used to dilute the magnitude of measurement errors, and therefore, is also more useful in practical viewpoint. Moreover, the independence of measurement error and covariate is not required in our theorems. An experimental design with measurement error satisfying the required degenerating rate is introduced. In addition, this assumption allows us to employ sequential sampling, which is popular in clinical trials, to such a measurement error logistic regression model. It is clear that the sequential method cannot be applied based on the assumption that the measurement errors decay uniformly as sample size increasing as in the most of the literature. Therefore, a sequential estimation procedure based on MLEs and such moment conditions is proposed and can be shown to be asymptotical consistent and efficient. Case-control studies are broadly used in clinical trials and epidemiological studies. It can be showed that the odds ratio can be consistently estimated with some exposure variables based on logistic models (see Prentice and Pyke (1979)). The two-stage case-control sampling scheme is employed for a confidence region of slope coefficient beta. A necessary sample size is calculated by a given pre-determined level. Furthermore, we consider the measurement error in the covariates of a case-control retrospective logistic regression model. We also derive some asymptotic results of the maximum likelihood estimators (MLEs) of the regression coefficients under some moment conditions on measurement errors. Under such kinds of moment conditions of measurement errors, the MLEs can be shown to be strongly consistent, asymptotically unbiased and asymptotically normally distributed. Some simulation results of the proposed two-stage procedures are obtained. We also give some numerical studies and real data to verify the theoretical results in different measurement error scenarios.

實施十二年國民基本教育，目的是為促進學生五育均衡發展，兼顧國中學習品質及日常生活表現。由於各校對成績的評分標準與評分方式皆不相同，因此如何使在校成績採計達到公平性將成為一項重要的問題。 戴岑熹(2011) 考慮了國中在校綜合學科分數與基測總分間的相關性，以決定在校各學科的權重。而本研究延伸其概念與方法，將基測各科量尺分數考慮進來，於在校綜合學科分數與基測綜合量尺分數的關聯性最密切的情況下，分析各學科權重的取決方式，希望能找出較理想的模式來代表學生在校三年的整體學習表現與成果，以做為免試升學採計在校成績的參考與依據。 本文的研究方法是運用典型相關分析的理論，但因權重的限制條件與傳統典型相關分析的要求不同，因此，便將其命名為「類典型相關分析」。在類典型相關分析中，我們證明了在校各學科分數及基測各科量尺分數的最佳權重，可先透過典型相關分析求得典型相關向量，若有必要的話，使用Rao-Ghangurad 方法加以修正，最後，再將所獲得的非負典型相關向量正規化，即可獲得所要的結果，這是一個求最佳權重向量極便捷的途徑。在實例分析方面，我們發現了一個有趣的現象，即在校學科分數與基測考科量尺分數的最佳權重向量相當接近，即名稱相同的學科與考科幾乎有相同的權重。在比較了幾個權重分配方式不同的在校綜合學科分數後，我們也發現一般學校常用的等加權模式，其表現結果也頗優異。 / The purpose of implementing the twelve-year compulsory education is to promote the balanced development of learning in students, taking into account their learning quality and normal daily performances in school. As the evaluation standard and method vary among schools, achieving fairness in calculating in-school grades has become an important issue. Dai (2011) considered the correlations between the scores of in-school academic performance and the total score of the BCTEST for junior high schools, which decided to the weightings of all learning subjects. This study extended his concept and method, and took into account the scale scores of all learning subjects. In the closest case of the weightings of all learning subjects and find out the correlations between the scores of in-school academic performance and the BCTEST, and analyse the weightings of all learning subjects. We hope the study can find a better approach that can not only reflect students’ learning situations and achievements for the three years in school but also provide a reference for the evaluation of entering senior high schools without entrance examinations. The research method in this paper employs the theory of canonical correlation analysis.However, due to that fact that weight restrictions are different from the requirements of canonical correlation analysis, it is named as the canonical correlation analysis type approach. In the canonical correlation analysis type approach, we proved that the optimal weights for school subject score and test subject score scales can be obtained by finding the canonical correlation vectors using canonical correlation analysis. Then the Rao-Ghangurad method can further be used for amending, if needed. Finally, the nonnegative canonical correlation vectors generated would be normalized to get the desired result. It is an extremely convenient way to obtain the optimal weight vector. In the case study, we found an interesting phenomenon as follows: When the optimal weight vectors for school subject score and test subject score scales were very close, subjects and tests of the same name had almost the same weight. After comparing several comprehensive school subject scores of different weight distribution, we also found that the results of the equal weighting model commonly used in schools also showed quite good results.

近來三維數值城市及數碼城市（Cyber City）為各界極欲發展及研究的課題，為了要增加三維數值城市的擬真性及美觀程度，通常是將建物模型敷貼真實拍攝之牆面影像，增加三維模型的細緻化程度。而欲精確的敷貼牆面紋理影像，必須嚴密地將所拍攝之近景影像定位定向，一般採用光束法區域平差解算，此時需加上適當的控制點控制資訊才能完成，因此控制點控制資訊若來自地面測量將相當耗費成本。多年來，各地方政府製作大比例尺地形圖時已拍攝相當多的航照影像，可用來做為上述的控制資訊，亦即航空影像控制實體，若能使用這些航空影像控制實體作為控制資訊，不但可有效利用資源，亦能減少控制點取得所需花費的成本。因此，本研究將使用航空影像控制實體所提供的控制資訊做為控制來源。 本研究探討以航空影像控制實體作為控制資訊時，使用非量測型相機以類似傳統航測拍攝方式及旋轉多基線交向拍攝方式拍攝涵蓋建物牆面的目標區影像後，於最少控制且不同控制分布時，對光束法區域平差精度之影響。因使用非量測型相機，故本研究先以iWitnessPRO近景攝影測量軟體率定相機參數，接著以PHIDIAS近景攝影測量軟體解算光束法區域平差。過程中探討使用航空影像控制實體作為控制資訊時，於最少控制且不同控制分布時，加入附加參數解算的自率光束法區域平差與與一般光束法區域平差之精度。根據實驗結果，低樓層取像的光束法區域平差之檢核點RMSE精度，其結果大多可應用於LOD 3精度等級的牆面敷貼。另，因都市地區高樓林立，狹小巷弄多，有鑒於此，本研究使用旋轉多基線交向攝影，結果顯示其將有機會運用於近景攝影測量LOD 3精度等級的牆面紋理敷貼。 / Recently, the studies about the cyber city have become a popular topic. For improving the level of detail of cyber city, photo-realistic textures from images are mapped onto the surfaces of 3D building models. Before the accurate texture mapping, bundle block adjustment can be performed to recover the parameters of exterior orientation for each close-range images more accurate and more precise, where the control information is necessary. For the past years, many aerial photogrammetry projects were done by local governments for the mapping of 1/1000 topographic maps. Those historic aerial images can be used as control information to reduce the cost and increase the efficiency. Therefore, this study investigates the accuracy of bundle block adjustment about non-metric close-range images, taken from the ways similar to the traditional aerial photogrammetry and the rotating multi-baseline photogrammetry, by using control entities from historic aerial images as the minimal controls under various control distributions. Since the non-metric camera is used for collecting the close-range images, the iWitnessPRO software is utilized for camera calibration. After that, the PHIDIAS software, a close-range photogrammetry software, is employed to performed the bundle block adjustment. During performing the bundle block adjustment, the camera parameters are regarded as unknowns and determined, called as self-calibration bundle adjustment. The results of self-calibration bundle adjustment will be compared with conventional bundle adjustment. The test results show that the accuracy of most self-calibration bundle adjustment about close-range images covered with low buildings can be used for the application of LOD 3 texture mapping. Moreover, the test results of using close-range images from rotating multi-baseline photogrammetry in urban areas show the potential possibility for LOD 3 texture mapping in urban areas with high buildings and narrow alleys.