In some nonlinear regression situations, one or more of the parameters in the expression for the regression function are estimated from a separate data source. In such a case, the typical procedure is to estimate the appropriate parameters from the separate data and then to plug these estimated values into the expression for the regression function in order to estimate the other parameters. This situation arises frequently in compartment modeling when there is an external "input function" to the system. Issues in estimation of parameters and their standard errors will be discussed. Both asymptotic and bootstrap-based approaches will be presented and compared.
This work is applicable in a variety of real-data situations. One important application is the estimation of kinetic parameters in an alternative "model-free" formulation of a standard pharmacokinetic model for PET imaging data. In this case (and in standard pharmacokinetic fitting cases), the model is fit to each of several regions of interest in the brain and the "input function" is estimated from data obtained from an arterial line. Approaches to estimation of parameters and their standard errors in this situation will be presented and discussed. (This is a joint work with Thaddeus Tarpey, Department of Mathematics and Statistics, Wright State University.)
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.