Nonparametric Estimation of the Singularities of a Signal from Noisy Measurements
نویسندگان
چکیده
We study a problem of locating and estimating singularities of a signal measured with noise on a discrete set of points (fixed-design model). The signal consists of a smooth part with bounded first derivative and of finite number of singularities of the type (x ti)p±d¡■, 0 < p < j . The case p = 0 corresponds to a piecewise continuous function. The algorithm is based on convolving the data with a kernel having compact support. Optimal bandwidth of the kernel is calculated, the consistency of the algorithm is proved. The results of testing the proposed algorithm on model examples are presented.
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