Variance Estimation for High-Dimensional Regression Models

The paper is concerned with the problem of variance estimation for a high-dimensional regression model. The results show that the accuracy n-1/2 of variance estimation can be achieved only under some restrictions on smoothness properties of the regression function and on the dimensionality of the model. In particular, for a two times differentiable regression function, the rate n-1/2 is achievable only for dimensionality smaller or equal to 8. For a higher dimensional model, the optimal accuracy is n-4/d which is worse than n-1/2. The rate optimal estimating procedure is presented.