  We consider the problem of sequentially learning to estimate, in the mean
squared error (MSE) sense, a Gaussian $K$-vector of unknown covariance by
observing only $m < K$ of its entries in each round. We first establish a
concentration bound for MSE estimation. We then frame the estimation problem
with bandit feedback, and propose a variant of the successive elimination
algorithm. We also derive a minimax lower bound to understand the fundamental
limit on the sample complexity of this problem.
