《微分几何在影响分析中的应用（英文版）》讨论微分几何在统计学影响分析中的应用，适合数学及统计学本科生或研究生阅读。对于研习数学的学生，本书描述微分几何在数学范畴以外的具体应用；对于研习统计的学生，本书则能帮助他们理解统计领域中的微分几何概念。

《微分几何在影响分析中的应用（英文版）》要求读者具备线性代数及向量微积分的基础知识。书的第一部分围绕法曲率、截面曲率和高斯曲率概念介绍了图的几何 学知识；第二部分回顾了统计学的一些基本概念及模型，为理解影响分析提供必要的基础知识；第三部分则集中讨论上述几何概念在局部影响分析中的应用，并探讨 如何有效地应用几何概念以提高局部影响分析估计的效力。

《微分几何在影响分析中的应用（英文版）》为研习统计学或数学的学生架起了知识理解的桥梁，为数学与统计学的跨学科研究合作及相互推进发挥创新性的作用。

前辅文
Part I Geometry
  1 Preliminaries
   1.1 Linear algebra
   1.2 Vector calculus
  2 Euclidean Geometry
   2.1 Orthogonal transformations
   2.2 Rigid motions
   2.3 Translation of vector subspaces
   2.4 Conformal transformations
   2.5 Orthonormal basis
   2.6 Orthogonal projections
   2.7 Areas and volumes
  3 Geometry of Graphs
   3.1 Graphs in Euclidean spaces
   3.2 Normal sections
   3.3 Cross sections in high dimension
   3.4 First fundamental forms
  4 Curvatures
   4.1 Normal curvatures
   4.2 Sectional curvatures
  5 Transformations and Invariance
   5.1 Change of coordinates
   5.2 Non-linear conformal transformations
   5.3 Invariant curvatures
Part II Statistics
  6 Discrete Random Variables and Related Concepts
   6.1 Preliminaries
   6.2 Discrete random variables
   6.3 Population parameters and sample statistics
   6.4 Mathematical expectations
   6.5 Maximum likelihood estimation
   6.6 Maximum likelihood estimation of the probability of a Bernoulli experiment
  7 Continuous Random Variables and Related Concepts
   7.1 Continuous random variables
   7.2 Mathematical expectation for continuous random variables
   7.3 Mean and variance and their sample estimates
   7.4 Basic properties of expectations
   7.5 Normal distribution
   7.6 Maximum likelihood estimation for continuous variables
   7.7 Maximum likelihood estimation for the parameters of normal distribution
   7.8 Sampling distribution
  8 Bivariate and Multivariate Distribution
   8.1 Bivariate distribution for discrete random variables
   8.2 Bivariate distribution for continuous random variables
   8.3 Mathematical expectations
   8.4 Covariance and correlation
   8.5 Bivariate normal distribution
   8.6 Independence
   8.7 Multivariate distribution
  9 Simple Linear Regression
   9.1 The model
   9.2 The least squares estimation
   9.3 The maximum likelihood estimation of regression parameters
   9.4 Residuals
   9.5 Coefficient of determination
   9.6 Weighted least squares estimates
  10 Topics on Linear Regression Analysis
   10.1 Multiple regression model
   10.2 Estimation and interpretation
   10.3 Influential observations and outliers
   10.4 Leverage
   10.5 Cook's distance
   10.6 Deletion influence, joint influence and masking effect
   10.7 Derivation of Cook's distances
Part III Local Influence Analysis
  11 Basic Concepts
   11.1 Introduction
   11.2 Perturbation
   11.3 Likelihood displacement and influence graph
  12 Measuring Local Influence
   12.1 Individual influence
   12.2 Derivation of normal curvature
   12.3 Case-weight perturbation—an example
   12.4 Roles of sectional curvature
   12.5 Joint influence
  13 Relations Among Various Measures
   13.1 A bound on influence measures
   13.2 Individual and overall joint influence
   13.3 Individual and joint influence measures
   13.4 Competing eigenvalues
   13.5 Conclusions
  14 Conformal Modifications
   14.1 Modification and invariance
   14.2 Invariant measures
   14.3 Benchmarks
   14.4 Individual's contribution to joint influence—re-visited
Appendix A Rank of Hat Matrix
Appendix B Ricci Curvature
Appendix C Cook's Distance—Deleting Two Data Points
Bibliography
Index

现代数学纵览SMM