A Moving Ellipsoid Method for Nonparametric Regression and its Application to Logit Diagnostics with Scanner Data
作者提出了一种新的非参数回归方法，移动椭球法，用于平滑回归曲面。该方法在核回归基础上，沿回归曲面切向方向优先平滑，从而在保持回归灵活性的同时，改善平均绝对偏差和回归平滑性。作者将这一方法应用于品牌选择建模，通过构造多项逻辑模型中随机项的实证分布，并与理论分布比较，提供了一种类似OLS回归中检验残差正态性的逻辑模型一致性检验。
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.