Functional Measurement Error Models Research Articles

Effect of measurement error in testing separate linear models

Measurement error models (or errors-in variables models) have been explored since the latter part of the 19th century. Much activity and results in estimation and statistical inference have been forthcoming in linear and non-linear measurement error models, particularly in the past 10 to 15 years. Likewise, tests of separate families of hypotheses have received much attention sice Cox (1961, 1962) introduced a method of testing separate families of hypotheses. The aim of this paper is to provide results for testing separate linear models using Cox's methodology under the assumption of the functional measurement error model for which the error structure has a normal distribution. Simulations are used to compare the results of the Cox test when using estimates adjusted for measurement error, naive estimats, and estimates derived from true values. The overall conclusions derived from the simulation results are mixed. However, if the measurement error is small and collinearity between explanatory variables fr...

An alternative approach to estimation in the functional measurement error problem

A method is proposed which simplifies estimation of all parameters in the functional measurement error model with no error in the equation under the assumption that the error covariance for the explanatory variables is known and the variance of the dependent variable is unknown. the proposed method is shown to produce the same estimates given for the both the structural model and the functional model with error in the eqution in schneeweiss (1976) and fuller (1987). Simulation results indicate that for large sample sizes and even for moderate sample sizes, the maximum likelihood regression estimates one gets from assuming a structural measurement error model perform quite well in estimating the regression parameters in the functional measurement error model.

Approximating Fisher's information for the functional measurement error model

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.