A Moving Ellipsoid Method for Nonparametric Regression and its Application to Logit Diagnostics with Scanner Data

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Abstract
Nonparametric regression becomes increasingly attractive for marketing applications as the required large databases become available. The well-known kernel method provides the regression E(y|x) of a response variable y given explanatory variables x. A new, moving ellipsoid variant smooths the regression surface preferentially along the tangential direction of E(y|x). The method generalizes the flexible regression technique and provides improvements in mean absolute deviation and/or regression smoothness. In an application to brand choice modeling, the ellipsoid method constructs an empirical distribution of the stochastic term in a multinomial logit model. Comparison of empirical and theoretical distributions provides a consistency test for the logit model analogous to examining the normality of residuals in OLS regression.

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