## The Annals of Statistics

### Maximin effects in inhomogeneous large-scale data

#### Abstract

Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients, where the change is either smoothly in time or some other dimension or even without any such structure. Fitting varying-coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return more information than necessary. If we just ask for a model estimator that shows good predictive properties for all regimes of the data, then we are aiming for a simple linear model that is reliable for all possible subsets of the data. We propose the concept of “maximin effects” and a suitable estimator and look at its prediction accuracy from a theoretical point of view in a mixture model with known or unknown group structure. Under certain circumstances the estimator can be computed orders of magnitudes faster than standard penalized regression estimators, making computations on large-scale data feasible. Empirical examples complement the novel methodology and theory.

#### Article information

Source
Ann. Statist., Volume 43, Number 4 (2015), 1801-1830.

Dates
Revised: November 2014
First available in Project Euclid: 17 June 2015

https://projecteuclid.org/euclid.aos/1434546223

Digital Object Identifier
doi:10.1214/15-AOS1325

Mathematical Reviews number (MathSciNet)
MR3357879

Zentralblatt MATH identifier
1317.62059

Subjects
Primary: 62J07: Ridge regression; shrinkage estimators

#### Citation

Meinshausen, Nicolai; Bühlmann, Peter. Maximin effects in inhomogeneous large-scale data. Ann. Statist. 43 (2015), no. 4, 1801--1830. doi:10.1214/15-AOS1325. https://projecteuclid.org/euclid.aos/1434546223

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