Isotonic regression with unknown permutations: Statistics, computation, and adaptation

  title={Isotonic regression with unknown permutations: Statistics, computation, and adaptation},
  author={Ashwin Pananjady and Richard J. Samworth},
Motivated by models for multiway comparison data, we consider the problem of estimating a coordinate-wise isotonic function on the domain $[0, 1]^d$ from noisy observations collected on a uniform lattice, but where the design points have been permuted along each dimension. While the univariate and bivariate versions of this problem have received significant attention, our focus is on the multivariate case $d \geq 3$. We study both the minimax risk of estimation (in empirical $L_2$ loss) and the… 

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