Soft Maximin Estimation for Heterogeneous Array Data.

The extraction of a common signal across many recordings is difficult when each recording -- in addition to the signal -- contains large, unique variation components. Maximin estimation has previously been proposed as a robust estimation method in the presence of heterogeneous noise. We propose soft maximin estimation as a computationally attractive methodology for estimating a common signal from heterogeneous data. The soft maximin loss is introduced as an aggregation, controlled by a parameter $\zeta>0$, of explained variances and the estimator is obtained by minimizing the penalized soft maximin loss. By establishing statistical and computational properties we argue that the soft maximin method is a statistically sensibel and computationally attractive alternative to existing methods. In particular we demonstrate, on simulated and real data, that the soft maximin estimator can outperform existing methods both in terms of predictive performance and run time. We also provide a time and memory efficient implementation for data with array-tensor structure in the R package SMMA available on CRAN.