Dimension Reduction in Binary Response Regression
研究了在二元响应回归中，如何通过切片逆回归、主Hessian方向等方法估计中心子空间，实现无信息损失的降维，并生成充分汇总图。
Abstract The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Focusing on the central subspace, we investigate such "sufficient" dimension reduction in regressions with a binary response. Three existing methods—sliced inverse regression, principal Hessian direction, and sliced average variance estimation—and one new method—difference of covariances—are studied for their ability to estimate the central subspace and produce sufficient summary plots. Combining these numerical methods with the graphical methods proposed earlier by Cook leads to a novel paradigm for the analysis of binary response regressions. Key Words: Dimension-reduction subspaceLinear combinations of chi-squared variablesRegression graphicsSliced inverse regressionPrincipal Hessian directionSliced average variance estimation.