Nonparameteric Regression Splines for Generalized Linear Measurement Error Models

In many regression applications both the independent and dependent variables are measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. This is further complicated when one instead wants to fit a generalized linear model to the collected data. We consider two different estimation techniques. The first method is the SIMEX (SIMulation Extrapolation) algorithm which attempts to estimate the bias, and remove it. The second method is a structural approach, where one hypothesizes a distribution for the independent variable which depends on estimable parameters. For both methods, two different knot selection methods are developed.