Adaptive estimation of High-Dimensional Signal-to-Noise Ratios

  title={Adaptive estimation of High-Dimensional Signal-to-Noise Ratios},
  author={Nicolas Verzelen and Elisabeth Gassiat},
We consider the equivalent problems of estimating the residual variance, the proportion of explained variance η and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand the impact of not knowing the sparsity of the regression coefficient and not knowing the distribution of the design on minimax estimation rates of η. Depending on the sparsity k of the regression coefficient, optimal estimators of η either rely on estimating the… CONTINUE READING