# Estimation of a regression function when the observations contain measurement errors: Berkson vs classical errors.

*by Dr Aurore Delaigle*

*Institution:*University of Bristol and the Univerity of Melbourne

*Date: Wed 4th April 2007*

*Time: 11:00 AM*

*Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne*

*Abstract*: A regression function is a curve that describes the relation between two random variables. There exist many techniques to estimate such

a curve from a sample of accurate observations, i.e. where the variables are measured precisely. In real life applications, however, it happens very often that the observations can only be measured approximately.

In such cases, it is common to assume that the measurement error is of "classical type", i.e. the observed value W is a random perturbation of the variable X of interest (i.e. W=X+U with U and X independent).

In many epidemiologic studies, however, the roles of X and W are inverted and the errors are rather of Berkson type: here, it is the unobservable

X that is a random perturbation of W. Although the two types of errors look

similar, the methodology used to estimate a curve with classical errors is not valid in the case of Berkson errors. We discuss a technique of regression estimation for Berkson errors, based on orthogonal series approximations.

*For More Information:* Paul A. Pearce Email: P.Pearce@ms.unimelb.edu.au or Felisa Vazquez-Abad 8344 0012