Effect of mean on variance function estimation in nonparametric regression
By Lie Wang, Lawrence D. Brown, Tommaso Cai, Michael Levine. 2008
126 citations recorded by the source corpus.
Variance function estimation in nonparametric regression is considered and the minimax rate of convergence is derived. We are particularly interested in the effect of the unknown mean on the estimation of the variance function. Our results indicate that, contrary to the common practice, it is not desirable to base the estimator of the variance function on the residuals from an optimal estimator of the mean when the mean function is not smooth. Instead it is more desirable to use estimators of the mean with minimal bias. On the other hand, when the mean function is very smooth, our numerical results show that the residual-based method performs better, but not substantial better than the first-order-difference-based estimator. In addition our asymptotic results also correct the optimal rate claimed in Hall and Carroll [J. Roy. Statist. Soc. Ser. B51 (1989) 3-14].
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/247c75577e5066261721f5e3b36e6b81818d447e
How researchers see this paper
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In Statistics and Probability
- Tommaso Cai
- A. van der Vaart
- E. T. Tchetgen Tchetgen
- Edward H. Kennedy
- James M. Robins
- Lingling Li
- Richard Nickl
- Mark G. Low
Citations in the corpus
- Higher order influence functions and minimax estimation of nonlinear functionals (2008, background): “[27], consider the difference-based estimator”
- Model-free model-fitting and predictive distributions (2010, background): “Note, however, that the choice q = h is not necessarily optimal; see e.g. Wang et al. (2008).”
- Variance estimation in nonparametric regression via the difference sequence method (2007, methodology): “In the special case where γ = 2 and β = 1, the finite sample performance of this estimator has been investigated in Levine [25] together with the possible choice of bandwidth.”
- Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional (2011, background): “See, for example, Cai and Low (2005) and Wang et al. (2008).”