Streamline: 统计学学习与进阶

[关于统计学专业的学习进阶]

1. Introductory
   1.1 Introduction to Statistical Reasoning
   　　统计学概念（实验设计、描述统计、相关和回归、概率、抽样、机会模型、显著性检验等）
   　　Textbook: Seeing Through Statistics, Jessica M. Utts, 2008
   1.2 Introduction to Statistics
   　　定量分析方法（概率、抽样分布理论、线性回归、方差分析、置信区间、假设检验等）、软件使用
   　　Textbook: Stats: data and models, De Veaux Richard D, 2016
　　Textbook: Elementary Statistics, Allan G Bluman, 2008
   1.3 Calculus-based Introduction to Statistics
   　　统计概念+数学（随机变量、概率分布、pdf、cdf、均值、方差、相关性、条件分布、条件均值、条件方差、正态分布、卡方分布、F分布、t分布、大数定律、中心极限定理、参数估计、无偏性、一致性、有效性、假设检验、p值、置信区间、极大似然估计等）
   　　Textbook: Probability and statistics for engineering and the sciences, Devore Jay L, 2016
   1.4 Introduction to Probability and Statistics
   　　概率论与统计推断（概率模型、随机变量、分布、条件、期望、大数定律、中心极限定理、点估计、区间估计、假设检验、线性回归）
   　　Textbook: Probability and statistics for engineering and the sciences, Devore Jay L, 2016

2. Applied statistics concentration
   2.1 Applied Statistical Computing
   　　R软件编程
   2.2 Applied Linear Regression Analysis
   　　回归分析及其实现（简单回归、非线性回归、logistic模型、随机效应模型）
   　　Textbook: Applied linear regression models, Kutner Michael etc., 2004
　　Textbook: Linear models with R, Julian J Faraway, 2005
   2.3 Applied Categorical Data Analysis
   　　分类数据的分析及其实现（多项分布、列联表、logistic回归、log-linear模型、graphical方法）
   　　Textbook: An introduction to categorical data analysis, Agresti Alan, 2007
   2.4 Applied Statistical Methods
   　　实践（模型的优劣、随机效应模型、混合效应模型、广义估计方法、over-dispersion、生存分析、power的计算）
   　　Textbook: Data analysis using regression and multilevel/hierarchical models, Gelman Andrew, 2007
   2.5 Applied Data Mining
   　　机器学习相关（预测、分类、神经网络）

3. Foundation
   3.1 Probability Theory
   　　Textbook: Probability and measure, Billingsley Patrick, 1995
　　Textbook: Probability and measure: anniversary edition, Billingsley, 2012
　　Textbook: Introduction to probability models, Ross Sheldon M, 2003
   3.2 Statistical Inference
   　　Textbook: Probability and statistics, Morris H Degroot, 2012
　　Textbook: Testing statistical hypotheses, Lehmann EL, 2005
　　Textbook: Asymptotic statistics, A W van der Vaart, 2000
   3.3 Linear Regression Models
   　　Textbook: Applied linear regression models, Kutner Michael H Nachtsheim, 2004
　　Textbook: Linear models with R, Julian J Faraway, 2005
   3.4 Statistical Computing and Introduction to Data Science
   3.5 Elementary Stochastic Processes
   　　Textbook: Introduction to probability models, Ross Sheldon M, 2003

4. Advanced statistics
   4.1 Time Series Analysis
   　　时间序列（平滑、预测、傅立叶分析、谱估计、脉冲响应、转换函数、自相关函数、Box-Jenkins建模和预测）
   　　Textbook: Analysis of financial time series, Ruey S Tsay, 2010
　　Textbook: Introduction to time series and forecasting, Peter J Brockwell, 2002
　　Textbook: Multivariate time series analysis: with R and financial applications, Ruey S Tsay, 2014
　　Textbook: Time series: theory and methods, Peter J Brockwell, 2006
   4.2 Nonparametric Statistics
   　　不需要参数模型假定（rank, permutation, order）
   4.3 Multivariate Statistical Inference
   　　多元正态分布、多元回归及分类、典型相关(canonical correlation)分析、graphical模型、贝叶斯网络、主成分分析、因子分析、SVD、判别分析、聚类分析
   　　Textbook: Applied multivariate statistical analysis, Hardle, 2015
　　Textbook: Modern multivariate statistical techniques: regression, classification and manifold learning, Lzenman Alan Julian, 2008
   4.4 Bayesian analysis
   　　先验信息、分层模型、线性模型、非线性模型
   　　Textbook: Bayesian data analysis, Gelman Andrew, 2011
　　Textbook: Probability and statistics, Morris H deGroot, 2012
   4.5 Survival Analysis
   　　生存分布、删失数据、生存模型、非参数估计
   　　Textbook: Survival analysis: techniques for censored and truncated data, Klein John P, 2003
   4.6 Multilevel Models
   　　随机效应/混合效应模型及其模型诊断
   4.7 Sample Surveys
   　　抽样调查的设计和分析（抽样设计、结果分析）
   　　Textbook: Sampling: design and analysis, Lohr Sharon L, 2010
   4.8 Statistical Machine Learning
   　　机器学习算法及应用（大数据、计算机）
   4.9 Statistical Methods in Finance
   　　资产定价模型、多因子定价模型、主成分分析、多元分析、平滑技术、生产曲线估计
   　　Textbook: Statistics and data analysis for financial engineering : with R examples, Ruppert David, 2015
   4.10 Statistical Inference and Time Series Modelling
   　　Textbook: Regression modelling with actuarial and financial applications, Eward W Frees, 2010
   4.11 Advanced Data Analysis
   　　探索数据分析、建模、拟合优度检验、线性回归、方差分析、非线性回归、广义线性模型、生存分析、时间序列分析、现代回归方法
   　　Textbook: The Statistical Sleuth: A Course in Methods of Data Analysis, Fred Ramsey, 2012
   4.12 Generalized Linear Models
   　　广义线性模型（rates, proportions, 定序变量、无序变量、列联表、odds-ratios、exact inference、logistic回归、poisson回归）
   　　Textbook: Categorical data analysis, Agresti Alan, 2012

5. Advanced data science
   5.1 Statistical Machine Learning
   5.2 Advanced Machine Learning
   5.3 Applied Data Science
   　　Textbook: The elements of statistical learning: data mining, inference and prediction, Trevor Hastie, 2009
   5.4 Exploratory Data Analysis and Visulization
   　　Textbook: Graphical data analysis with R, Unwin Antony, 2015

6. Advanced Stochastic Processes
   6.1 Stochastic Processes for Finance
   　　Textbook: Arbitrage theory in continuous time, Bjork Tomas, 2009
   6.2 Stochastic Processes and Applications
   　　Textbook: Pricing and hedging of derivative securities, Lars Tyge Nielsen, 1999
　　Textbook: Stochastic calculus for Finance II: continuous-time models, Steven E Shreve, 2010
   6.3 Stochastic Methods in Finance
   　　Textbook: Stochastic calculus for finance, Steven E Shreve, 2005