Special Colloquia, Department of Statistics Thursday, January 23, 2003 in MATH 175 4:30 PM Mr. Michael Levine University of Pennsylvania will speak on A New Local Variance Estimator for Nonparametric Regression Abstract Traditionally, non-parametric regression research has been centered on the mean estimation problem. As a rule, the variance is presumed to be an unknown constant and then one of several standard estimators is proposed to estimate it. Very often, though, the homoscedasticity assumption is not viable. To build a confidence or a prediction interval, we need to have precise enough local variance estimator. This serves as a reason to look for a reliable local variance estimator when the data is heteroscedastic. In this talk I present a simple difference-based kernel estimator for the local variance function in the nonparametric regression setup. It is shown that, asymptotically, its mean squared error is independent of the mean function. This allows us to estimate the variance function without knowing the mean. The asymptotic mean squared error has the familiar convergence rate of the order -4/5 while the bandwidth is of the order -1/5. A crossvalidation - type bandwidth selection procedure is introduced and illustrated on simulated data sets. Finally, the practical use of the estimator is illustrated using a Logincome vs. Age data set from the Canadian Census of 1971, a call center service times data set and a Treasury Bill yield data set. Refreshments will be available in MATH Library at 4:15 p.m.

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