In nonparametric signal estimation, there is a need for estimating the logarithmic probability density derivatives. This problem is complex, because the logarithmic density derivative is a function with singularity-a ratio containing density in the denominator. Since the density estimate can take values close or even equal to zero, the estimate of the logarithmic derivative becomes unstable. This difficulty is surmounted by constructing a new nonparametric estimate for the logarithmic derivative, i.e., an estimate that is stable to observation and based piecewise-smooth approximation. Its properties for dependent observations generated by stationary processes satisfying the strong mixing condition are studied. The rate of convergence of the nonparametric estimate and the principal part of the expansion of the mean-square estimate error are determined.
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