A Dimension Reduction Approach to the Study of City Family-income Distributions Via Sliced Inverse Regression.

Sliced inverse regression is a dimension reduction technique for exploring non-linear relationships between an output variable and a vector of input variables. Motivated by a data set of income distributions and economic indicators of french cities, we adress the problem of modelling a family of empirical distribution functions in terms of some covariates. SIR allows us to visually explore the ralationship between the covariates and several important features of the income distributions. A stochastic ordering is revealed for the French city income distributions.