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Partition-wise models offer a flexible approach for modeling complex and multidimensional data and are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with a simple submodel. The success of this approach highly depends on the quality of the partition, as too large a region could lead to a nonsimple submodel, while too small a region could inflate estimation variance. This paper proposes an automatic procedure for choosing the partition (i.e., the number of regions and the boundaries between regions) as well as the submodels for the regions. It is shown that under the assumption of the existence of a true partition, as well as a set of known significant predictors, the proposed partition estimator is statistically consistent. Features of the proposed methodology are highlighted for both regression and classification problems on synthetic and real data. [ABSTRACT FROM PUBLISHER]

This article proposes new model-fitting techniques for quantiles of an observed data sequence, including methods for data segmentation and variable selection. The main contribution, however, is in providing a means to perform these two tasks simultaneously. This is achieved by matching the data with the best-fitting piecewise quantile regression model, where the fit is determined by a penalization derived from the minimum description length principle. The resulting optimization problem is solved with the use of genetic algorithms. The proposed, fully automatic procedures are, unlike traditional break point procedures, not based on repeated hypothesis tests, and do not require, unlike most variable selection procedures, the specification of a tuning parameter. Theoretical large-sample properties are derived. Empirical comparisons with existing break point and variable selection methods for quantiles indicate that the new procedures work well in practice. [ABSTRACT FROM PUBLISHER]