http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/193 Tue, 07 Apr 2026 11:21:01 GMT 2026-04-07T11:21:01Z http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67958 標題: 高維度平均-變異數最佳化之共變異數矩陣估計:以台灣資料為例; Variance-Covariance Matrix Estimation for High Dimensional Mean-Variance Optimization: Evidence from Taiwan 作者: Han Chiu; 裘涵 摘要: 在平均-變異數投資組合最佳化的問題中，我們時常需要估計共變異數矩陣的反矩陣以計算投資組合的最適權重。當資產數量大且樣本數小的同時，共變異數矩陣在計算反矩陣上較為困難且複雜。常用來估計高維度共變異數矩陣的方法是在樣本共變異數上利用稀疏性假設，使高維度矩陣轉換為一個可逆矩陣。本研究提出一個統計框架，透過修正的Cholesky 分解法將高維度共變異數矩陣估計，轉換為迴歸係數估計之問題，並使用正交貪婪演算法(OGA)處理高維度迴歸模型之選擇。在模擬研究中，比較估計量與母體共變異數矩陣間的差異。此外，實證研究顯示在合理的參數假設下，OGA 估計結果優於Adaptive thresholding和linear shrinkage之方法。; The classical mean-variance portfolio optimization requires the estimation of an inverse covariance matrix. This is a challenging task given the large number of assets in the market and at the same time limited available historical data. Commonly used methods for estimating large covariance matrix exploit sparsity in the sample covariance matrix. In this study, I propose a statistical framework to estimate high-dimensional variance-covariance matrices under small sample size via the modified Cholesky decomposition with orthogonal greedy algorithm (OGA). This study transforms the covariance matrix estimation into a regression coefficient estimation problem, where the OGA is a fast stepwise regression method for the high-dimensional model selection and coefficient estimation. Therefore, I perform simulation studies to measure the difference between the estimators and the population covariance matrix. Moreover, empirical results show OGA estimators have better performance than adaptive thresholding and linear shrinkage approaches under reasonable parameter assumptions. Sun, 01 Jan 2017 00:00:00 GMT http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67958 2017-01-01T00:00:00Z http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91684 標題: 順序尺度依變數與自變數估計方法的再檢視; Reexamination of Estimation Methods for Ordinal Dependent and Independent Variables 作者: 林韋廷; Wei-Ting Lin 摘要: 實證研究者通常將順序尺度的依變數和自變數視為數值資料或名目尺度資料進行分析，然而這些處理方式分別高估和低估了資料所包含的資訊，因此在理論和實務上都存在一些缺陷。本研究探討順序尺度資料的分析方法，並嘗試在貝氏統計方法框架下探索更適合處理順序尺度資料的統計方法，包括累積probit模型和順序尺度自變數的單調性處理，以確保模型反映出依變數與自變數的順序尺度特性。 本研究使用「臺灣農村社會文化調查計畫分項一：人口、社會與經濟調查計畫」於2019年收集之調查資料，該調查共完成3,321份農村居民問卷調查。以順序尺度的「生活滿意程度」作為依變數，示範統計建模中切點、係數等參數的先驗分配設定，將順序尺度的自變數「家庭經濟狀況」作單調性處理，並透過模型的配適結果探討自變數對於生活滿意程度的影響。本研究透過套件brms計算不同順序尺度自變數資料處理方法下累積probit模型的配適結果，並以捨一交叉確認法比較了不同模型的適合度。 本文最後提供順序尺度依變數與順序尺度自變數在統計建模與資料處理上的建議，以及實際應用上模型比較的判斷依據。本研究還提供了使用R語言進行分析的程式碼，以便其他研究者能夠重現本文的結果，或在根據需求調整後應用於相關研究。; Researchers in empirical studies often interpret ordinal dependent and independent variables as either metric or nominal data. However, these methods are susceptible to both overestimating and underestimating the information inherent in the data, resulting in certain theoretical and practical constraints. The current study examined methods appropriate for the analysis of ordinal data and attempts to search statistical models better suited for handling ordinal data within a Bayesian framework. In line with this, I employed cumulative probit models and incorporated monotonic effects for ordinal independent variables to precisely capture the ordinal characteristics of both dependent and independent variables. This study utilized data from “A Social and Cultural Survey of Rural Taiwan: Sub-project ‘Population, Society and Economy Survey’ (2019)”, consisting of 3,321 rural residents. The dependent variables, life satisfaction, was measured on an ordinal scale to demonstrate the setting of prior distributions for cutpoints, coefficients, and other parameters in statistical modeling. The ordinal independent variable, family economic status, undergoes monotonicity treatment, and the fitted results of the model are used to explore the impact of independent variables on life satisfaction. The brms package in R is employed to compute the fitted results of the cumulative probit model under different data processing methods for ordinal independent variables, and model comparison is conducted using leave-one-out cross-validation. In the conclusion section, this study proposes recommendations for the statistical modeling and data processing of ordinal dependent and independent variables. It also establishes criteria for model comparison in practical applications. Furthermore, the study includes R code for analysis, allowing fellow researchers to replicate the results or modify them for similar studies according to their specific requirements. Mon, 01 Jan 2024 00:00:00 GMT http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91684 2024-01-01T00:00:00Z http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93233 標題: 非歐幾何之投資組合風險平衡策略：流形學習與網絡分析; Non-Euclidean geometric portfolio theory and risk parity: Manifold learning and network analysis 作者: 趙俊程; Chun-Cheng Chao 摘要: 本研究結合流形學習與網絡分析方法，以資產間的網絡關係做為量化風險指標，作一創新的風險平價投資組合策略。本研究利用等距特徵映射來捕捉資產之間的非歐幾何距離，並利用距離相關度量揭示資產間的非線性關係，為資產配置提供更深入的分析基礎。 為了對相關係數矩陣進行降維，我們採用三角最大濾圖 (Triangulated Maximally Filtered Graph）對網絡進行過濾，保留更具有代表性的主要風險結構。利用圖論衡量資產節點的子圖中心性，以及關注負向風險損失的條件風險價值(Expected Shortfall)，構建考慮全局及個體的防護性資產配置。 在產業龍頭存股等權重指數作為回測資料上，我們的方法展現出更優異的風險調整後收益，突顯出使用非歐幾何與網絡分析在投資組合風險管理方面的潛力與創新性。; This study integrates manifold learning and network analysis to quantify risk using asset network relationships, creating an innovative risk parity portfolio strategy. Isometric Mapping (Isomap) is employed to capture non-Euclidean distances and reveal nonlinear relationships between assets. The Triangulated Maximally Filtered Graph (TMFG) is applied to filter the network, retaining the most representative risk structures. By measuring assets' subgraph centrality and considering the Expected Shortfall, we construct a defensive asset allocation. As for backtesting part, we using the Taiwan Industrial Leaders Dividend Equal Weight Index demonstrates superior risk-adjusted returns, highlighting the potential of non-Euclidean geometry and network analysis in portfolio risk management. Mon, 01 Jan 2024 00:00:00 GMT http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93233 2024-01-01T00:00:00Z http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71995 標題: 電阻脈衝感應之隨機程序模型; A Stochastic Modeling of Nanopore Resistive Pulse Sensing 作者: Tzu-Hui Lin; 林子暉 摘要: 奈米孔道在生物科技上的應用非常廣泛，由於其特殊的電動力學現象，使得奈米粒子、分子或者DNA鹼基對在接近奈米孔道時的電泳行為相當複雜。阻抗脈衝的技術便是奈米孔道的相關應用，目前已廣泛被用於測定粒子的大小、形狀、表面電位等等，以往有許多文章從脈衝訊號的大小與形狀來判斷粒子的各項性質，而本研究從隨機程序的模型切入，透過觀察粒子通過奈米孔道時產生訊號的頻率與間隔，估計其通過奈米孔道中不同位置時之電泳速度。粒子受外加電場驅動後具有電泳速度，在裝置中的各個位置之速度不盡相同，透過卜瓦松過程來描述特定位置截面通過的粒子數量，藉以觀察粒子在不同區域時的速度。但由於粒子在特定位置的數量將影響卜瓦松過程的參數，且此裝置為一多階層卜瓦松過程，其對於時間之機率分配難以描述。本研究利用特殊之運算方式，計算各個位置粒子數量之期望值，進而了解粒子在不同位置速度之關係，藉以觀察粒子之各項性質。; Nanopore research has a various application in biotechnology. Electrophoresis of nanoparticles, molecules, or DNA base pairs around nanopore is rather complicated due to particular electrodynamics. Nanopore resistive pulse sensing has been used to characterize the size, shape or zeta potential of nanoparticles. Much research has been conducted to determine the property of a particle through the shape and size of a pulse. In this study, we use the frequency and interval of pulses to build a stochastic process to estimate the electrophoresis of particles. However, the procedure of nanopore resistive pulse sensing is a multi-step poisson process which includes event-dependent parameter, it is hard to get the probability distribution under such circumstance. We use a special method to calculate the expected value of numbers of particles and therefore to estimate the properties of particles. Mon, 01 Jan 2018 00:00:00 GMT http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71995 2018-01-01T00:00:00Z