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On simple wavelet estimators of random signals and their small-sample properties

In the paper we suggest certain nonparametric estimators of random signals based on the wavelet transform. We consider stochastic signals embedded in white noise and extractions with wavelet denoizing algorithms utilizing the non-decimated discrete wavelet transform and the idea of wavelet scaling. We evaluate properties of these estimators via extensive computer simulations and partially also analytically. Our wavelet estimators of random signals have clear advantages over parametric maximum likelihood methods as far as computational issues are concerned, while at the same time they can compete with these methods in terms of precision of estimation in small samples. An illustrative example concerning smoothing of survey data is also provided.