Date of Award
Doctor of Philosophy
Wayne A. Fuller
The measurement error model with heterogeneous error variances is considered. Theory for estimators constructed with weighting functions is developed for the case where there is an error in the regression equation and for the case when the equation in the unknown true values is exact. The limiting distribution of the properly standardized weighted estimators is shown to be that of a standard multivariate normal random variable. The limit is taken as the error variances become small and the sample size becomes large.;The specific case where the weighting function is the inverse of a variance function that depends on the true but unknown values of the independent variable is examined. Both linear and non-linear variance functions are examined.;An example is presented in which there are non-homogeneous measurement error variances that increase with the value of the independent variable. The variances of the error variances are expressed as a non-linear function of the true values of the independent variable. Weights based on this function are used to construct estimators of the parameters of the model.;Monte Carlo studies using data similar to that of the example are employed to assess the adequacy of the asymptotic approximations in small samples. In this example the error variance is about eight percent of the total variance of the explanatory variable. Weighting improves the estimators in samples of fifty observations, but the Studentized statistics require larger samples in order for the distribution to well approximate that of Student's t for the type of data used.;A computer program for weighting the observed values by estimated variances is described. The program is equipped to handle data from complex surveys and to estimate the parameters for models with and without an error in the equation. The program also is capable of outputting the estimated true values and standardized residuals.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Nancy Ann Eyink Hasabelnaby
Hasabelnaby, Nancy Ann Eyink, "The use of a weighting function in measurement error regression " (1987). Retrospective Theses and Dissertations. 8651.