Measurement Error in Nonlinear ModelsThis monograph provides an up-to-date discussion of analysis strategies for regression problems in which predictor variables are measured with errors. The analysis of nonlinear regression models includes generalized linear models, transform-both-sides models and quasilikelihood and variance function problems. The text concentrates on the general ideas and strategies of estimation and inference rather than being concerned with a specific problem. Measurement error occurs in many fields, such as biometry, epidemiology and economics. In particular, the book contains a large number of epidemiological examples. An outline of strategies for handling progressively more difficult problems is also provided. |
Contents
REGRESSION CALIBRATION | 40 |
SIMULATION EXTRAPOLATION | 79 |
INSTRUMENTAL VARIABLES | 107 |
FUNCTIONAL METHODS | 122 |
LIKELIHOOD AND QUASILIKELIHOOD | 141 |
BAYESIAN METHODS | 165 |
SEMIPARAMETRIC METHODS | 182 |
UNKNOWN LINK FUNCTIONS | 199 |
HYPOTHESIS TESTING | 206 |
DENSITY ESTIMATION AND NONPARAMET | 215 |
RESPONSE VARIABLE ERROR | 229 |
OTHER TOPICS | 243 |
A FITTING METHODS AND MODELS | 257 |
| 280 | |
| 298 | |
Common terms and phrases
additive algorithm American Statistical Association analysis applications assumed assumption asymptotic Bayesian Berkson bias bootstrap Carroll Chapter coefficient complete data components compute consistent estimate covariance matrix covariates measured data set deconvolution define denote density estimates described distributed with mean estimating equations estimating function Exam example extrapolant Framingham data functional modeling Gibbs sampler given heteroscedastic homoscedastic instrumental variable intake least squares linear models linear regression logistic regression M-estimator M₁ maximum likelihood mean and variance measured with error measurement error models measurement error variance methods missing data naive test nonlinear nonparametric regression normally distributed observed data posterior predictors problem pseudolikelihood quadratic quasilikelihood regression calibration approximation regression calibration model regression model replicates resampling response sample sandwich saturated fat score test SIMEX SIMEX estimator ẞo ẞt ẞz standard errors Stefanski structural modeling surement error surrogate tion validation data variance function vector W₁