Deconvolution problems in nonparametric statistics /
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| Author / Creator: | Meister, Alexander. |
|---|---|
| Imprint: | Berlin : Springer, c2009. |
| Description: | vi, 210 p. ; 24 cm. |
| Language: | English |
| Series: | Lecture notes in statistics ; 193 Lecture notes in statistics (Springer-Verlag) ; 193. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7784352 |
Table of Contents:
- 1. Introduction
- 2. Density Deconvolution
- 2.1. Additive Measurement Error Model
- 2.2. Estimation Procedures
- 2.2.1. Kernel Methods
- 2.2.2. Wavelet-based Methods
- 2.2.3. Ridge-Parameter Approach
- 2.3. General Consistency
- 2.4. Optimal Convergence Rates
- 2.4.1. Smoothness Classes/Types of Error Densities
- 2.4.2. Mean Squared Error: Upper Bounds
- 2.4.3. Mean Integrated Squared Error: Upper Bounds
- 2.4.4. Asymptotic Normality
- 2.4.5. Mean Squared Error: Lower Bounds
- 2.4.6. Mean Integrated Squared Error: Lower Bounds
- 2.5. Adaptive Bandwidth Selection
- 2.5.1. Cross Validation
- 2.6. Unknown Error Density
- 2.6.1. Deterministic Constraints
- 2.6.2. Additional Data
- 2.6.3. Replicated Measurements
- 2.7. Special Problems
- 2.7.1. Heteroscedastic Contamination
- 2.7.2. Distribution and Derivative Estimation
- 2.7.3. Other Related Topics
- 3. Nonparametric Regression with Errors-in-Variables
- 3.1. Errors-in-Variables Problems
- 3.2. Kernel Methods
- 3.3. Asymptotic Properties
- 3.3.1. Consistency
- 3.3.2. Optimal Convergence Rates
- 3.4. Berkson Regression
- 3.4.1. Discrete-Transform Approach
- 3.4.2. Convergence Rates
- 4. Image and Signal Reconstruction
- 4.1. Discrete Observation Scheme and Blind Deconvolution
- 4.2. White Noise Model
- 4.3. Circular Model and Boxcar Deconvolution
- A. Tools from Fourier Analysis
- A.1. Fourier Transforms of L1(R)-Functions
- A.2. Fourier Transforms of L2(R)-Functions
- A.3. Fourier Series
- A.4. Multivariate Case
- B. List of Symbols
- References
