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Subsampling
Springer Series in Statistics
ISBN/EAN: 9780387988542
Umbreit-Nr.: 5540140
Sprache:
Englisch
Umfang: xv, 348 S.
Format in cm:
Einband:
gebundenes Buch
Erschienen am 13.08.1999
Auflage: 1/1999
- Zusatztext
- InhaltsangabeI Basic Theory.- 1 Bootstrap Sampling Distributions.- 1.1 Introduction.- 1.1.1 Pivotal Method.- 1.1.2 Asymptotic Pivotal Method.- 1.1.3 Asymptotic Approximation.- 1.1.4 Bootstrap Approximation.- 1.2 Consistency.- 1.3 Case of the Nonparametric Mean.- 1.4 Generalizations to Mean-like Statistics.- 1.5 Bootstrapping the Empirical Process.- 1.6 Differentiability and the Bootstrap.- 1.7 Further Examples.- 1.8 Hypothesis Testing.- 1.9 Conclusions.- 2 Subsampling in the I.I.D. Case.- 2.1 Introduction.- 2.2 The Basic Theorem.- 2.3 Comparison with the Bootstrap.- 2.4 Stochastic Approximation.- 2.5 General Parameters and Other Choices of Root.- 2.5.1 Studentized Roots.- 2.5.2 General Parameter Space.- 2.6 Hypothesis Testing.- 2.7 Data-Dependent Choice of Block Size.- 2.8 Variance Estimation: The Delete-d Jackknife.- 2.9 Conclusions.- 3 Subsampling for Stationary Time Series.- 3.1 Introduction.- 3.2 Univariate Parameter Case.- 3.2.1 Some Motivation: The Simplest Example.- 3.2.2 Theory and Methods for the General Univariate Parameter Case.- 3.2.3 Studentized Roots.- 3.3 Multivariate Parameter Case.- 3.4 Examples.- 3.5 Hypothesis Testing.- 3.6 Data-Dependent Choice of Block Size.- 3.7 Bias Reduction.- 3.8 Variance Estimation.- 3.8.1 General Statistic Case.- 3.8.2 Case of the Sample Mean.- 3.9 Comparison with the Moving Blocks Bootstrap.- 3.10 Conclusions.- 4 Subsampling for Nonstationary Time Series.- 4.1 Introduction.- 4.2 Univariate Parameter Case.- 4.3 Multivariate Parameter Case.- 4.4 Examples.- 4.5 Hypothesis Testing and Data-Dependent Choice of Block Size.- 4.6 Variance Estimation.- 4.7 Conclusions.- 5 Subsampling for Random Fields.- 5.1 Introduction and Definitions.- 5.2 Some Useful Notions of Strong Mixing for Random Fields.- 5.3 Consistency of Subsampling for Random Fields.- 5.3.1 Univariate Parameter Case.- 5.3.2 Multivariate Parameter Case.- 5.4 Variance Estimation and Bias Reduction.- 5.5 Maximum Overlap Subsampling in Continuous Time.- 5.6 Some Illustrative Examples.- 5.7 Conclusions.- 6 Subsampling Marked Point Processes.- 6.1 Introduction.- 6.2 Definitions and Some Different Notions on Mixing.- 6.3 Subsampling Stationary Marked Point Processes.- 6.3.1 Sampling Setup and Assumptions.- 6.3.2 Main Consistency Result.- 6.3.3 Nonstandard Asymptotics.- 6.4 Stochastic Approximation.- 6.5 Variance Estimation via Subsampling.- 6.6 Examples.- 6.7 Conclusions.- 7 Confidence Sets for General Parameters.- 7.1 Introduction.- 7.2 A Basic Theorem for the Empirical Measure.- 7.3 A General Theorem on Subsampling.- 7.4 Subsampling the Empirical Process.- 7.5 Subsampling the Spectral Measure.- 7.6 Conclusions.- II Extensions, Practical Issues, and Applications.- 8 Subsampling with Unknown Convergence Rate.- 8.1 Introduction.- 8.2 Estimation of the Convergence Rate.- 8.2.1 Convergence Rate Estimation: Univariate Parameter Case.- 8.2.2 Convergence Rate Estimation: Multivariate Parameter Case.- 8.3 Subsampling with Estimated Convergence Rate.- 8.4 Conclusions.- 9 Choice of the Block Size.- 9.1 Introduction.- 9.2 Variance Estimation.- 9.2.1 Case of the Sample Mean.- 9.2.2 General Case.- 9.3 Estimation of a Distribution function.- 9.3.1 Calibration Method.- 9.3.2 Minimum Volatility Method.- 9.4 Hypothesis Testing.- 9.4.1 Calibration Method.- 9.4.2 Minimum Volatility Method.- 9.5 Two Simulation Studies.- 9.5.1 Univariate Mean.- 9.5.2 Linear Regression.- 9.6 Conclusions.- 9.7 Tables.- 10 Extrapolation, Interpolation, and Higher-Order Accuracy.- 10.1 Introduction.- 10.2 Background.- 10.3 I.I.D. Data: The Sample Mean.- 10.3.1 Finite Population Correction.- 10.3.2 The Studentized Sample Mean.- 10.3.3 Estimation of a Two-Sided Distribution.- 10.3.4 Extrapolation.- 10.3.5 Robust Interpolation.- 10.4 I.I.D. Data: General Statistics.- 10.4.1 Extrapolation.- 10.4.2 Case of Unknown Convergence Rate to the Asymptotic Approximation.- 10.5 Strong Mixing Data.- 10.5.1 The Studentized Sample Mean.- 10.5.2 Estimation of a Two-Sided Distribution.- 10.5.3 The Unstudent
- Autorenportrait
- InhaltsangabeI Basic Theory.- 1 Bootstrap Sampling Distributions.- 1.1 Introduction.- 1.1.1 Pivotal Method.- 1.1.2 Asymptotic Pivotal Method.- 1.1.3 Asymptotic Approximation.- 1.1.4 Bootstrap Approximation.- 1.2 Consistency.- 1.3 Case of the Nonparametric Mean.- 1.4 Generalizations to Mean-like Statistics.- 1.5 Bootstrapping the Empirical Process.- 1.6 Differentiability and the Bootstrap.- 1.7 Further Examples.- 1.8 Hypothesis Testing.- 1.9 Conclusions.- 2 Subsampling in the I.I.D. Case.- 2.1 Introduction.- 2.2 The Basic Theorem.- 2.3 Comparison with the Bootstrap.- 2.4 Stochastic Approximation.- 2.5 General Parameters and Other Choices of Root.- 2.5.1 Studentized Roots.- 2.5.2 General Parameter Space.- 2.6 Hypothesis Testing.- 2.7 Data-Dependent Choice of Block Size.- 2.8 Variance Estimation: The Delete-d Jackknife.- 2.9 Conclusions.- 3 Subsampling for Stationary Time Series.- 3.1 Introduction.- 3.2 Univariate Parameter Case.- 3.2.1 Some Motivation: The Simplest Example.- 3.2.2 Theory and Methods for the General Univariate Parameter Case.- 3.2.3 Studentized Roots.- 3.3 Multivariate Parameter Case.- 3.4 Examples.- 3.5 Hypothesis Testing.- 3.6 Data-Dependent Choice of Block Size.- 3.7 Bias Reduction.- 3.8 Variance Estimation.- 3.8.1 General Statistic Case.- 3.8.2 Case of the Sample Mean.- 3.9 Comparison with the Moving Blocks Bootstrap.- 3.10 Conclusions.- 4 Subsampling for Nonstationary Time Series.- 4.1 Introduction.- 4.2 Univariate Parameter Case.- 4.3 Multivariate Parameter Case.- 4.4 Examples.- 4.5 Hypothesis Testing and Data-Dependent Choice of Block Size.- 4.6 Variance Estimation.- 4.7 Conclusions.- 5 Subsampling for Random Fields.- 5.1 Introduction and Definitions.- 5.2 Some Useful Notions of Strong Mixing for Random Fields.- 5.3 Consistency of Subsampling for Random Fields.- 5.3.1 Univariate Parameter Case.- 5.3.2 Multivariate Parameter Case.- 5.4 Variance Estimation and Bias Reduction.- 5.5 Maximum Overlap Subsampling in Continuous Time.- 5.6 Some Illustrative Examples.- 5.7 Conclusions.- 6 Subsampling Marked Point Processes.- 6.1 Introduction.- 6.2 Definitions and Some Different Notions on Mixing.- 6.3 Subsampling Stationary Marked Point Processes.- 6.3.1 Sampling Setup and Assumptions.- 6.3.2 Main Consistency Result.- 6.3.3 Nonstandard Asymptotics.- 6.4 Stochastic Approximation.- 6.5 Variance Estimation via Subsampling.- 6.6 Examples.- 6.7 Conclusions.- 7 Confidence Sets for General Parameters.- 7.1 Introduction.- 7.2 A Basic Theorem for the Empirical Measure.- 7.3 A General Theorem on Subsampling.- 7.4 Subsampling the Empirical Process.- 7.5 Subsampling the Spectral Measure.- 7.6 Conclusions.- II Extensions, Practical Issues, and Applications.- 8 Subsampling with Unknown Convergence Rate.- 8.1 Introduction.- 8.2 Estimation of the Convergence Rate.- 8.2.1 Convergence Rate Estimation: Univariate Parameter Case.- 8.2.2 Convergence Rate Estimation: Multivariate Parameter Case.- 8.3 Subsampling with Estimated Convergence Rate.- 8.4 Conclusions.- 9 Choice of the Block Size.- 9.1 Introduction.- 9.2 Variance Estimation.- 9.2.1 Case of the Sample Mean.- 9.2.2 General Case.- 9.3 Estimation of a Distribution function.- 9.3.1 Calibration Method.- 9.3.2 Minimum Volatility Method.- 9.4 Hypothesis Testing.- 9.4.1 Calibration Method.- 9.4.2 Minimum Volatility Method.- 9.5 Two Simulation Studies.- 9.5.1 Univariate Mean.- 9.5.2 Linear Regression.- 9.6 Conclusions.- 9.7 Tables.- 10 Extrapolation, Interpolation, and Higher-Order Accuracy.- 10.1 Introduction.- 10.2 Background.- 10.3 I.I.D. Data: The Sample Mean.- 10.3.1 Finite Population Correction.- 10.3.2 The Studentized Sample Mean.- 10.3.3 Estimation of a Two-Sided Distribution.- 10.3.4 Extrapolation.- 10.3.5 Robust Interpolation.- 10.4 I.I.D. Data: General Statistics.- 10.4.1 Extrapolation.- 10.4.2 Case of Unknown Convergence Rate to the Asymptotic Approximation.- 10.5 Strong Mixing Data.- 10.5.1 The Studentized Sample Mean.- 10.5.2 Estimation of a Two-Sided Distribution.- 10.5.3 The Unstudent