Department of Mathematics

# Nonregular semiparametrics for Gaussian white noise models

Ismael Castillo
(Vrije Universiteit Amsterdam)

20 November 2007

In this talk I will present a joint work with Eric Cator (TU Delft) on semiparametric white noise models. For instance let us consider estimation in the model $dX(t) = f(t-\theta)dt + \epsilon dW(t) , t\in[-1/2,1/2]$, where $f$ is a unknown symmetric 1-periodic square-integrable function, $\theta$ is the parameter of interest, $W$ is standard Brownian motion and $\veps$ tends to zero. When $f$ is smooth, it is known that the best possible rate in a minimax sense is a constant times $\veps$, rate which coincides with the parametric one. When $f$ is not assumed to be smooth, then usually one obtains in the parametric case fast rates of convergence: for instance if $f$ is a symmetric step-function, it is possible to estimate $\theta$ at rate $\epsilon2$. In our work we consider the problem of estimation in the semiparametric situation, for non-smooth $f$.

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Charlene Kalle