Inverse Problems and High-Dimensional Estimation
Pierre. Alquier
Bok Engelsk 2011 · Electronic books.
| Annen tittel | |
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| Utgitt | Berlin : Springer , 2011
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| Omfang | 1 online resource (203 p.)
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| Opplysninger | Description based upon print version of record.. - Inverse Problemsand High-Dimensional Estimation; Preface; The "Stats in the Chˆateau" Summer School; Inverse Problems and High-Dimensional Estimation; The Proceedings; Acknowledgments; Contents; List of Contributors; Part I Lecture Notes on Inverse Problems; Chapter 1 Inverse Problems in Statistics; Abstract; Preface; 1.1 Inverse Problems; 1.1.1 Introduction; 1.1.2 Statistical Inverse Problems; 1.1.3 Linear Inverse Problems with Random Noise; 1.1.4 Basic Notions on Operator Theory; 1.1.5 Singular Value Decomposition and Sequence Space Model; 1.1.6 Examples. - 1.1.6.1 Standard GaussianWhite Noise1.1.6.2 Derivation; 1.1.6.3 Circular Deconvolution; 1.1.6.4 Heat Equation; 1.1.6.5 Computerized Tomography; 1.1.7 Spectral Theory; 1.1.7.1 The Spectral Theorem; 1.1.7.2 Deconvolution on; 1.1.7.3 Functional Calculus; 1.2 Nonparametric Estimation; 1.2.1 Minimax Approach; 1.2.2 Regularization Methods; 1.2.2.1 Continuous RegularizationMethods; 1.2.2.2 Estimation Procedures; Equivalence in the Sequence Space Model; Truncated SVD; Kernel Estimator; The Tikhonov Estimator; The Landweber Method; The Pinsker Estimator; Risk of a Linear Estimator. - 1.2.3 Classes of Functions1.2.3.1 Source Conditions; 1.2.3.2 Ellipsoid of Coefficients; 1.2.3.3 Classes of Functions; 1.2.4 Rates of Convergence; 1.2.4.1 SVD Setting; 1.2.4.2 Deconvolution on; 1.2.5 Comparison Between Deterministic and Stochastic Noise; 1.3 Adaptation and Oracle Inequalities; 1.3.1 Minimax Adaptive Procedures; 1.3.2 Oracle Inequalities; Comments; 1.3.3 Model Selection; 1.3.3.1 Unbiased Risk Estimation; Comments; 1.3.3.2 Risk Hull Method; Comments; 1.3.3.3 Simulations; 1.3.4 Universal Optimality; 1.3.4.1 Blockwise Estimators; 1.3.4.2 Stein's Estimator. - 1.3.4.3 Blockwise Stein's Rules1.3.4.4 Construction of Blocks; 1.3.4.5 Model Selection Versus Universal Optimality Comments; 1.4 Conclusion; 1.4.1 Summary; 1.4.2 Discussion; 1.4.3 Open Problems; Noisy Operators; Nondiagonal Case; Wavelets and Sparsity; RHM for Other Methods; Nonlinear Operators; Error in Variables; Econometrics; Inverse Problems in Applications; Numerical Aspects; Well-Posed Questions; References; Part II Invited Contribution on Inverse Problems; Chapter 2 Non-parametric Models with Instrumental Variables; Abstract; 2.1 Introduction. - 2.2 The Linear Model: Vectorial or Functional Data2.3 The Additively Separable Model and Its Extensions; 2.4 The Non-separable Models; 2.5 Some Extensions to Dynamic Models; 2.6 Conclusion; References; Part III Lecture Notes on High-Dimensional Estimation; Chapter 3 High Dimensional Sparse Econometric Models: An Introduction; Abstract; 3.1 The High Dimensional Sparse Econometric Model; 3.2 The Setting and Estimators; 3.2.1 The Model; 3.2.2 LASSO and Post-LASSO Estimators; 3.2.3 Intuition and Geometry of LASSO and Post-LASSO; 3.2.4 Primitive Conditions; 3.3 Analysis of LASSO. - 3.4 Model Selection Properties and Sparsity of LASSO. - The ""Stats in the Chateau"" summer school was held at the CRC chateau on the campus of HEC Paris, Jouy-en-Josas, France, from August 31 to September 4, 2009. This event was organized jointly by faculty members of three French academic institutions a"" ENSAE ParisTech, the Ecole Polytechnique ParisTech, and HEC Paris a"" which cooperate through a scientific foundation devoted to the decision sciences. The scientific content of the summer school was conveyed in two courses, one by Laurent Cavalier (Universite Aix-Marseille I) on ""Ill-posed Inverse Problems"", and one by Victor Chernozhukov (Ma
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 9783642199882
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