Nonparametric Estimation of Signal Amplitude in White Gaussian Noise

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We assume that a transmitted signal is of the form S(t)f(t), where f(t) is a known function vanishing at some points of the observation interval and S(t) is a function of a known smoothness class. The signal is transmitted over a communication channel with additive white Gaussian noise of small intensity ε. For this model, we construct an estimator for S(t) which is optimal with respect to the rate of convergence of the risk to zero as ε → 0.

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