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Serguei Pergamenchtchikov

Publications and source records attributed to Serguei Pergamenchtchikov.

24 records · Page 2Linked to original sources
arXiv2010

Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression

The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating an unknown nonparametric regression. %\cite{GaPe1}. We prove that this procedure is asymptotically efficient for a quadratic risk, i.e. the asymptotic quadratic risk for this procedure coincides with the Pinsker constant which gives a sharp lower bound for the quadratic risk over all possible estimates

math.ST↗
arXiv2009

Nonparametric estimation in a semimartingale regression model. Part 2. Robust asymptotic efficiency

In this paper we prove the asymptotic efficiency of the model selection procedure proposed by the authors in the first part. To this end we introduce the robust risk as the least upper bound of the quadratical risk over a broad class of observation distributions. Asymptotic upper and lower bounds for the robust risk have been derived. The asymptotic efficiency of the procedure is proved. The Pinsker constant is found.

math.ST↗
arXiv2008

Nonparametric estimation for an autoregressive model

The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for proposed estimators are shown.

math.ST↗
arXiv2004

The tail of the stationary distribution of a random coefficient AR(q) model

We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the model is in distribution equivalent to an autoregressive process with ARCH errors. Hence, we obtain the tail behavior of any such model of arbitrary order.

math.PR↗