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Wavelet Based Estimation of the Derivatives of a Density for a Discrete-Time Stochastic Process: Lp-Losses.

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We propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for such estimators. We suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quadratic characteristic.

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