Measurement Error ModelsJohn Wiley & Sons, 25 sept. 2009 - 480 pages The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "The effort of Professor Fuller is commendable . . . [the book] provides a complete treatment of an important and frequently ignored topic. Those who work with measurement error models will find it valuable. It is the fundamental book on the subject, and statisticians will benefit from adding this book to their collection or to university or departmental libraries." -Biometrics "Given the large and diverse literature on measurement error/errors-in-variables problems, Fuller's book is most welcome. Anyone with an interest in the subject should certainly have this book." -Journal of the American Statistical Association "The author is to be commended for providing a complete presentation of a very important topic. Statisticians working with measurement error problems will benefit from adding this book to their collection." -Technometrics " . . . this book is a remarkable achievement and the product of impressive top-grade scholarly work." -Journal of Applied Econometrics Measurement Error Models offers coverage of estimation for situations where the model variables are observed subject to measurement error. Regression models are included with errors in the variables, latent variable models, and factor models. Results from several areas of application are discussed, including recent results for nonlinear models and for models with unequal variances. The estimation of true values for the fixed model, prediction of true values under the random model, model checks, and the analysis of residuals are addressed, and in addition, procedures are illustrated with data drawn from nearly twenty real data sets. |
Table des matières
1 A Single Explanatory Variable | 1 |
12 Measurement Variance Known | 13 |
13 Ratio of Measurement Variances Known | 30 |
14 Instrumental Variable Estimation | 50 |
15 Factor Analysis | 59 |
16 Other Methods and Models | 72 |
21 Bounds for Coefficients | 100 |
22 The Model with an Error in the Equation | 103 |
23 The Model with No Error in the Equation | 124 |
24 Instrumental Variable Estimation | 148 |
25 Modifications to Improve Moment Properties | 163 |
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Expressions et termes fréquents
Appendix 4.A approximate distribution Assume assumption B₁ chi-square random variable coefficient column computed consistent estimator constructed converges in distribution defined degrees of freedom denoted derivatives diagonal e₁ equation error covariance matrix error variances estimated covariance matrix estimated standard errors estimated variance estimator of ẞ Example f₁ factor model fixed hypothesis independent instrumental variable iteration k-dimensional known least squares estimator limiting distribution mator maximum likelihood estimator mean square method multivariate nonlinear least squares nonsingular normally distributed observations obtained ordinary least squares parameters plot population positive definite Proof random variable regression row vector sample covariance sample covariance matrix Section smallest root ẞ₁ standard errors statistic Theorem true values u₁ unbiased v₁ vech vech mzz W₁ X₁ x₁₁ y₁ Z₁ zero β₁ βι βο εε μχ Σεε σχχ นน