c © 2008, Indian Statistical Institute A Heteroscedastic Polynomial Regression with Measurement Error in Both Axes

With epidemiological and astronomical data, it is common to observe vari-ances that vary with the observations. Further, values for those variances typically are available from follow-up studies or replications. This paper deals with consistent estimation and hypothesis testing in a heteroscedas-tic polynomial model with measurement error in both axes and an equation error. For obtaining consistent estimators and consistently assessing their asymptotic variances, we embrace the corrected score approach. Further-more, we applied the theoretical results in two real data sets: the WHO MONICA project data set on cardiovascular diseases and their risk factors and the Chandra observatory data set. We also simulate the rejection rates for the Wald statistic in order to study test size and power for small and moderate samples, indicating that the test behaves satisfactorily in those situations. AMS (2000) subject classification. Primary 62J99; secondary 34K25