Local polynomial variance-function estimation
Technometrics
Variance function estimation in multivariate nonparametric regression with fixed design
Journal of Multivariate Analysis
On Nonparametric Residual Variance Estimation
Neural Processing Letters
Residual variance estimation in machine learning
Neurocomputing
Residual variance estimation using a nearest neighbor statistic
Journal of Multivariate Analysis
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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.