  Regression models that ignore measurement error in predictors may produce
highly biased estimates leading to erroneous inferences. It is well known that
it is extremely difficult to take measurement error into account in Gaussian
nonparametric regression. This problem becomes tremendously more difficult when
considering other families such as logistic regression, Poisson and
negative-binomial. For the first time, we present a method aiming to correct
for measurement error when estimating regression functions flexibly covering
virtually all distributions and link functions regularly considered in
generalized linear models. This approach depends on approximating the first and
the second moment of the response after integrating out the true unobserved
predictors in a semiparametric generalized linear model. Unlike previous
methods, this method is not restricted to truncated splines and can utilize
various basis functions. Through extensive simulation studies, we study the
performance of our method under many scenarios.
