Measurement error models /
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| Author / Creator: | Fuller, Wayne A. |
|---|---|
| Imprint: | New York : Wiley, c1987. |
| Description: | xxiii, 440 p. ; 24 cm. |
| Language: | English |
| Series: | Wiley series in probability and mathematical statistics. Probability and mathematical statistics |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/865060 |
Table of Contents:
- List of Examples
- List of Principal Results
- List of Figures
- 1. A Single Explanatory Variable
- 1.1. Introduction
- 1.1.1. Ordinary Least Squares and Measurement Error
- 1.1.2. Estimation with Known Reliability Ratio
- 1.1.3. Identification
- 1.2. Measurement Variance Known
- 1.2.1. Introduction and Estimators
- 1.2.2. Sampling Properties of the Estimators
- 1.2.3. Estimation of True x Values
- 1.2.4. Model Checks
- 1.3. Ratio of Measurement Variances Known
- 1.3.1. Introduction
- 1.3.2. Method of Moments Estimators
- 1.3.3. Least Squares Estimation
- 1.3.4. Tests of Hypotheses for the Slope
- 1.4. Instrumental Variable Estimation
- 1.5. Factor Analysis
- 1.6. Other Methods and Models
- 1.6.1. Distributional Knowledge
- 1.6.2. The Method of Grouping
- 1.6.3. Measurement Error and Prediction
- 1.6.4. Fixed Observed X
- Appendix 1.A. Large Sample Approximations
- Appendix 1.B. Moments of the Normal Distribution
- Appendix 1.C. Central Limit Theorems for Sample Moments
- Appendix 1.D. Notes on Notation
- 2. Vector Explanatory Variables
- 2.1. Bounds for Coefficients
- 2.2. The Model with an Error in the Equation
- 2.2.1. Estimation of Slope Parameters
- 2.2.2. Estimation of True Values
- 2.2.3. Higher-Order Approximations for Residuals and True Values
- 2.3. The Model with No Error in the Equation
- 2.3.1. The Functional Model
- 2.3.2. The Structural Model
- 2.3.3. Higher-Order Approximations for Residuals and True Values
- 2.4. Instrumental Variable Estimation
- 2.5. Modifications to Improve Moment Properties
- 2.5.1. An Error in the Equation
- 2.5.2. No Error in the Equation
- 2.5.3. Calibration
- Appendix 2.A. Language Evaluation Data
- 3. Extensions of the Single Relation Model
- 3.1. Nonnormal Errors and Unequal Error Variances
- 3.1.1. Introduction and Estimators
- 3.1.2. Models with an Error in the Equation
- 3.1.3. Reliability Ratios Known
- 3.1.4. Error Variance Functionally Related to Observations
- 3.1.5. The Quadratic Model
- 3.1.6. Maximum Likelihood Estimation for Known Error Covariance Matrices
- 3.2. Nonlinear Models with No Error in the Equation
- 3.2.1. Introduction
- 3.2.2. Models Linear in x
- 3.2.3. Models Nonlinear in x
- 3.2.4. Modifications of the Maximum Likelihood Estimator
- 3.3. The Nonlinear Model with an Error in the Equation
- 3.3.1. The Structural Model
- 3.3.2. General Explanatory Variables
- 3.4. Measurement Error Correlated with True Value
- 3.4.1. Introduction and Estimators
- 3.4.2. Measurement Error Models for Multinomial Random Variables
- Appendix 3.A. Data for Examples
- 4. Multivariate Models
- 4.1. The Classical Multivariate Model
- 4.1.1. Maximum Likelihood Estimation
- 4.1.2. Properties of Estimators
- 4.2. Least Squares Estimation of the Parameters of a Covariance Matrix
- 4.2.1. Least Squares Estimation
- 4.2.2. Relationships between Least Squares and Maximum Likelihood
- 4.2.3. Least Squares Estimation for the Multivariate Functional Model
- 4.3. Factor Analysis
- 4.3.1. Introduction and Model
- 4.3.2. Maximum Likelihood Estimation
- 4.3.3. Limiting Distribution of Factor Estimators
- Appendix 4.A. Matrix-Vector Operations
- Appendix 4.B. Properties of Least Squares and Maximum Likelihood Estimators
- Appendix 4.C. Maximum Likelihood Estimation for Singular Measurement Covariance
- Bibliography
- Author Index
- Subject Index
