顶部
  1. 首页
  2. 图书产品
  3. Application of Elementary Differential Geometry to Influence Analysis (微分几何在影响分析
收藏

Application of Elementary Differential Geometry to Influence Analysis (微分几何在影响分析

样章
作者：
潘日新 潘伟贤 著
定价：
59.00元
ISBN：
978-7-04-035700-4
版面字数：
250.000千字
开本：
16开
全书页数：
174页
装帧形式：
精装
重点项目：
暂无
出版时间：
2012-08-24
物料号：
35700-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数学与统计其他

《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
        • 1.1.1 Vectors and matrices
        • 1.1.2 Symmetric bilinear forms
        • 1.1.3 Vector subspaces
        • 1.1.4 Linear maps from Rn to Rn
        • 1.1.5 A convention
      • 1.2 Vector calculus
        • 1.2.1 Vector-valued functions and differentials
        • 1.2.2 Taylor expansion and extrema
        • 1.2.3 Extrema and Lagrange multiplier theorem
    • 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
        • 4.1.1 Definition
        • 4.1.2 Principal curvatures and principal directions
      • 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
        • 6.2.1 Discrete random variables and probability function
        • 6.2.2 Relative frequency histogram
        • 6.2.3 Cumulative distribution function
      • 6.3 Population parameters and sample statistics
        • 6.3.1 Population mean and expected value
        • 6.3.2 Sample statistic
        • 6.3.3 Sample mean
        • 6.3.4 Sample and population variances
      • 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
        • 8.1.1 Joint probability function
        • 8.1.2 Marginal probability function
        • 8.1.3 Conditional probability function
      • 8.2 Bivariate distribution for continuous random variables
      • 8.3 Mathematical expectations
        • 8.3.1 Mathematical expectations for the functions of two random variables
      • 8.4 Covariance and correlation
        • 8.4.1 Sample covariance and correlation
        • 8.4.2 Population covariance and correlation
        • 8.4.3 Conditional expectations
      • 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
        • 10.7.1 Weighted least squares and Cook's distance
        • 10.7.2 Cook's distance-deleting one data point
  • 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

相关图书

Geometric Structure of High-Dimensional Data and Dimensionality Reduction（海外销售版）

Jianzhong Wang

￥0.00 收藏

傅里叶分析(英文版)

Javier Duoandikoetxea

￥99.00 收藏

高阶傅里叶分析(英文版)

Terence Tao

￥99.00 收藏