Prediction and confidence intervals for nonlinear measurement error models without identifiability information

A major difficulty in applying a measurement error model is that one is required to have additional information in order to identify the model. In this paper, we show that there are cases in nonlinear measurement error models where it is not necessary to have additional information to construct prediction intervals for the future dependent variable Y and confidence intervals for the conditional expectation E(Y X) where X is the future observable independent variable. In particular, we consider two nonlinear models, the exponential and loglinear models. By applying pseudo-likelihood estimation of variance functions in the weighted least squares method, we construct theoretically justifiable prediction and confidence intervals in these two models. Some simulation results which show that the proposed intervals perform well are also provided.Measurement error models Prediction interval Confidence interval Exponential model Loglinear model Coverage probability