Variance estimation for high-dimensional regression models
- Spokoiny, Vladimir
2010 Mathematics Subject Classification
- 62G05 62G20
- variance estimation, regression, high dimension
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 higher dimensional model, the optimal accuracy is n-4/d which is worse than n-1/2. The rate optimal estimating procedure is presented.
- Journal of Multivariate Analysis, 82(2002), pp. 111-133