Approximating Fisher's information for the functional measurement error model

Abstract

For the functional measurement error model, the true, unobservable explanatory variables when treated as nuisance parameters yield an increase in the number of nuisance parameters corresponding to an increase in sample size. Fisher's information may not exist for all parameters under this scenario. We propose a simple but effective method of deriving Fisher's information by approximating the design matrix of explanatory variables with a quantile design matrix. We illustrate the application of our method with a numerical example. Adaptation of this method shows very good performance for the prediction problem.