We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal...
We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two
parameters. The first parameter governs the lacunarity of the wavelet
coefficients while the second one governs its intensity. In this paper,
we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal...
In this article we tackle the problem of inverse non linear ill-posed
problems from a statistical point of view. We discuss the problem
of estimating an indirectly observed function, without prior
knowledge of its regularity,
based on noisy observations. For this we
consider two
approaches: one based on the Tikhonov regularization procedure, and
another one based on model selection methods for both ordered and non
ordered subsets. In each case
we prove consistency of the estimators and show...
We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.
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