Regression and contrast estimated based on adaptive regressograms depending on qualitative explanatory variables

This methodological paper discusses the application of 'adaptive' non-parametric procedures for estimating regression functions or contrasts in situations with quantitative regressands and qualitative regressors. We propose to apply an adaptive regressogram, that is the selection of a regressogram estimate among the class of regressograms corresponding to all possible partitions of the regressor range. Our selection criterion is an analog to Mallows's Cp and this allows to state some small sample and asymptotic properties of the adaptive estimator. We also comment on stepwise selection procedures. The details of the procedure are presented in several interesting special cases, e.g. the two-or three-sample problem and the twoway classification. We illustrate there possible improvements over the usual least squares (ANOVA-)estimates.