Variance estimation in nonparametric regression via the difference sequence method
By Lawrence D. Brown, Michael Levine. 2007
144 citations recorded by the source corpus.
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.
Subfields: Artificial Intelligence, Numerical Analysis, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/cd9aa0e63bc75a37adcb2082ad1408b8ffd58674
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Demian Pouzo
- Tommaso Cai
- Xiaohong Chen
- Lie Wang
- Michael Levine
- Lawrence D. Brown
- Victor Chernozhukov
- Andrés Santos
In Numerical Analysis
In Statistics and Probability
- Demian Pouzo
- Xiaohong Chen
- Lawrence D. Brown
- Tommaso Cai
- Lie Wang
- Michael Levine
- Victor Chernozhukov
- Whitney K. Newey
Citations in the corpus
- Effect of mean on variance function estimation in nonparametric regression (2008, background): “Brown and Levine (2006) contains a detailed proof of this assertion for the case β = 2.”
- Adaptive variance function estimation in heteroscedastic nonparametric regression (2008, methodology): “As a special case, it is shown that the variance function estimator adaptively achieves the rate of convergence max { n−4α, ( logn n )2β/(1+2β)} (5) under both the pointwise MSE and global MISE, if f has α derivatives and V has β derivatives.”
- Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals (2009, background): “For alternative nonparametric variance estimators and their properties, see Robinson (1995b), Andrews (1995), Hall and Marron (1990), Brown and Levine (2007) and references therein.”