Large-scale data are often characterized by some degree of inhomogeneity asdata are either recorded in different time regimes or taken from multiplesources. We look at regression models and the effect of randomly changingcoefficients, where the change is either smoothly in time or some otherdimension or even without any such structure. Fitting varying-coefficientmodels or mixture models can be appropriate solutions but are computationallyvery demanding and often return more information than necessary. If we just askfor a model estimator that shows good predictive properties for all regimes ofthe data, then we are aiming for a simple linear model that is reliable for allpossible subsets of the data. We propose the concept of "maximin effects" and asuitable estimator and look at its prediction accuracy from a theoretical pointof view in a mixture model with known or unknown group structure. Under certaincircumstances the estimator can be computed orders of magnitudes faster thanstandard penalized regression estimators, making computations on large-scaledata feasible. Empirical examples complement the novel methodology and theory.
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