Statistics Seminar: Delaigle -- Estimation of a regression function when the observations contain measurement errors

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               *          UNIVERSITY OF SYDNEY              * 
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               *     SCHOOL OF MATHEMATICS & STATISTICS     *
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               *       STATISTICS SEMINAR SERIES - 2007     *
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              Estimation of a regression function 
       when the observations contain measurement errors:
                  Berkson vs classical errors 

             Aurore Delaigle (University of Bristol) 
              
                     May, 18 May, 2.00pm 

                         Carslaw 373 

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We consider density and regression estimation from a sample that contains measurement
errors.  In the classical context, the variable X of interest is observed with an error
that is independent and additive.  In other words, we observe W where W=X+U, with X and
U independent.  There are many practical examples where such a model can not reasonably
be assumed.  In many epidemiologic studies, for example, the erroneous observations are
such that the roles of X and W are inverted: in such problems, it is not possible to
measure the variable of interest, X, directly, and one rather measures another quantity,
W, that is linearly related to X.  For example, W could represent the concentration of a
toxic substance measured at several fixed stations, whereas the actual exposure of
individuals, X, varies around the concentrations at the stations.  In this second type
of problems, the errors are called Berkson errors.  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 techniques of regression estimation for
Berkson errors and a mixture of the two types of errors.  

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Enquiries about the Statistics Seminar: Rafal Kulik, rkuli@maths.usyd.edu.au