On matrix estimation under monotonicity constraints

  title={On matrix estimation under monotonicity constraints},
  author={Sabyasachi Chatterjee and Adityanand Guntuboyina and Bodhisattva Sen},
Abstract: We consider the problem of estimating an unknown n1×n2 matrix θ∗ from noisy observations under the constraint that θ∗ is nondecreasing in both rows and columns. We consider the least squares estimator (LSE) in this setting and study its risk properties. We show that the worst case risk of the LSE is n−1/2, up to multiplicative logarithmic factors, where n = n1n2 and that the LSE is minimax rate optimal (up to logarithmic factors). We further prove that for some special θ∗, the risk of… CONTINUE READING