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

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.