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非参数和半参数模型中的经验似然(英文版)
  • 书号:9787030278340
    作者:薛留根,朱力行
  • 外文书名:Empirical Likelihood in Nonparametric and Semiparametric Models
  • 丛书名:数学名著系列
  • 装帧:精装
    开本:B5
  • 页数:260
    字数:0
    语种:英文
  • 出版社:科学出版社
    出版时间:
  • 所属分类:O21 概率论与数理统计
  • 定价: ¥68.00元
    售价: ¥54.40元
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全书共分十章,依次为预备知识,单指标模型的经验似然,部分线性单指标模型的经验似然,经验似然半参数回归分析,变系数模型的经验似然,经验似然局部多项式回归分析,非线性EV模型的经验似然,线性模型的经验似然,响应均值的经验似然,半参数回归模型的经验似然。
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目录

  • Preface
    Chapter 1 Preliminary knowledge
    1.1 Empirical likelihood (EL)
    1.1.1 Definition of EL
    1.1.2 EL for mean
    1.1.3 Estimating equations
    1.1.4 Advantages of EL
    1.1.5 Related literature
    1.2 Bootstrap method
    1.3 Smoothing methods
    1.3.1 The Nadaraya-Watson estimator
    1.3.2 The local polynomial smoother
    1.4 Cross-validation
    1.4.1 Least squares cross-validation
    1.4.2 Generalized cross-validation
    1.5 Data sets
    1.5.1 Longitudinal data
    1.5.2 Measurement error data
    1.5.3 Missing data
    1.6 Some notations
    Chapter 2 EL for single-index models
    2.1 Introduction
    2.2 Methods and results
    2.2.1 Estimated EL
    2.2.2 Two adjusted EL ratios
    2.3 Simulation results
    2.4 Proofs
    2.4.1 Some lemmas
    2.4.2 Proofs of theorems
    Chapter 3 EL in a partially linear single-index model
    3.1 Introduction
    3.2 Methodology
    3.2.1 The general case
    3.2.2 Two special cases: single-index model and partially linear model
    3.3 Simulation results
    3.3.1 Preamble
    3.3.2 Simulated examples
    3.3.3 A real example
    3.4 Proofs
    3.4.1 A brief description of the proofs
    3.4.2 Proofs of theorems
    Chapter 4 EL semiparametric regression analysis
    4.1 Introduction
    4.2 Maximum EL estimator
    4.2.1 Estimating the regression coefficients
    4.2.2 Estimating the baseline function
    4.3 Confidence regions for regression coefficients
    4.3.1 Confidence regions based on normal approximation
    4.3.2 EL confidence region
    4.4 Confidence intervals for baseline function
    4.4.1 Normal approximation-based confidence interval
    4.4.2 Mean-corrected EL confidence interval
    4.4.3 Residual-adjusted EL confidence interval
    4.5 Numerical results
    4.5.1 Bandwidth choice
    4.5.2 Simulation studies
    4.5.3 An application
    4.6 Proofs
    Chapter 5 EL for a varying coefficient model
    5.1 Introduction
    5.2 Naive EL and maximum EL estimation
    5.2.1 Wilks\\\' phenomenon of naive EL
    5.2.2 Equivalence between MELE and WLSE
    5.3 Two bias corrections
    5.3.1 Mean-corrected EL
    5.3.2 Residual-adjusted EL
    5.4 Asymptotic confidence regions
    5.4.1 The general cases
    5.4.2 Partial profile EL for confidence intervals
    5.4.3 Simultaneous confidence bands
    5.4.4 Confidence regions based on the normal approximation
    5.4.5 Bootstrap confidence intervals and bands
    5.5 Numerical results
    5.5.1 Bandwidth choice
    5.5.2 Simulation studies
    5.5.3 The application to AIDS data
    5.6 Proofs of Theorems
    Chapter 6 EL local polynomial regression analysis
    6.1 Introduction
    6.2 Naive empirical likelihood
    6.2.1 Prime method
    6.2.2 Asymptotic properties
    6.3 A bias correction method
    6.4 Asymptotic confidence regions
    6.4.1 Confidence regions based on EL
    6.4.2 Pointwise confidence intervals based on partial EL
    6.4.3 Confidence regions based on the normal approximation
    6.4.4 Simultaneous confidence band
    6.5 Bandwidth selection
    6.5.1 Pilot bandwidth selection
    6.5.2 Refined bandwidth selection
    6.5.3 Undersmoothing bandwidth selection
    6.6 Numerical results
    6.6.1 Simulation study
    6.6.2 A real example
    6.7 Concluding remarks
    6.8 Proofs of Theorems
    Chapter 7 EL in nonlinear EV models
    7.1 Introduction
    7.2 Estimated EL
    7.3 Adjusted EL
    7.4 Simulations and application
    7.4.1 Simulations
    7.4.2 A real data example
    7.5 Conclusions
    7.6 Proofs
    Chapter 8 EL for the linear models
    8.1 Introduction
    8.2 EL for the regression coefficients
    8.2.1 EL with complete-case data
    8.2.2 Weighted EL
    8.2.3 EL with the imputed values
    8.2.4 Asymptotic properties
    8.3 EL for the response mean
    8.3.1 Weight-corrected EL
    8.3.2 Normal approximation
    8.4 Simulations
    8.4.1 One dimensional case
    8.4.2 Two dimensional case
    8.4.3 A real example
    8.5 Concluding remarks
    8.6 Proofs
    Chapter 9 EL for response mea
    9.1 Introduction
    9.2 Methods and results
    9.2.1 Weight-corrected EL
    9.2.2 Weight-corrected EL with auxiliary information
    9.2.3 Normal approximation-based method
    9.3 Simulations
    9.4 Concluding remarks
    9.5 Proofs
    Chapter 10 EL for a semiparametric regression model
    10.1 Introduction
    10.2 EL for the regression coefficients
    10.2.1 EL with complete-case data
    10.2.2 EL with the imputed values
    10.2.3 Partial profile empirical likelihood
    10.3 EL for the baseline function
    10.3.1 Estimated EL
    10.3.2 Residual-adjusted EL
    10.3.3 Simultaneous confidence band
    10.4 EL for the response mean
    10.4.1 Weight-corrected EL
    10.4.2 Normal approximation
    10.5 Simulations
    10.5.1 One-dimensional case
    10.5.2 Two-dimensional case
    10.6 Application
    10.7 Concluding remarks
    10.8 Proofs
    References
    Index
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