Variance estimation in high dimensional regression models

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Variance estimation in nonparametric regression via the difference sequence method (2007, unknown): “The Annals of Statistics 2007, Vol. 35, No. 5, 2219–2232 DOI: 10.1214/009053607000000145 © Institute of Mathematical Statistics, 2007”
On difference‐based variance estimation in nonparametric regression when the covariate is high dimensional (2005, background): “Our findings are related to a minimax result by Spokoiny (2002) who showed for twice differentiable regression functions that the √ N-rate is achievable only for d 8; otherwise the optimal rate is N−4=d .”