On system identification with nuisance parameters

Constructing proper confidence intervals is an important part of an estimation process. Sensitivity analysis, as in Friedlander (1990), provides a measure in mean-square-error as to how the maximum likelihood estimates of parameters of interest would change with changes in parameters not being estimated (i.e. nuisance parameters). This type of sensitivity analysis alone does not provide confidence intervals that include the uncertainty in nuisance parameters whereas nuisance parameter analysis presented in Spall (1989) and Spall and Garner (1990) does provide such confidence intervals. This note discusses the connection between these these two analyses.