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Simulation-extrapolation estimation in parametric measurement error models. (English) Zbl 0810.62028
Summary: We describe a simulation-based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated. The method entails adding additional measurement error in known increments to the data, computing estimates from the contaminated data, establishing a trend between these estimates and the variance of the added errors, and extrapolating this trend back to the case of no measurement error. We show that the method is equivalent or asymptotically equivalent to method-of-moments estimation in linear measurement error modeling. Simulation studies are presented showing that the method produces estimators that are nearly unbiased and efficient in standard and nonstandard logistic regression models. An oversimplified but fairly accurate description of the method is that it is method-of-moments estimation using Monte Carlo-derived estimating equations.

MSC:
62F10 Point estimation
62J02 General nonlinear regression
62J05 Linear regression; mixed models
65C05 Monte Carlo methods
62P10 Applications of statistics to biology and medical sciences; meta analysis
65C99 Probabilistic methods, stochastic differential equations
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