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We have previously proposed a novel order statistics correlation coefficient (OSCC), which possesses some desirable advantages when measuring linear and monotone nonlinear associations between two signals. However, the understanding of this new coefficient is far from complete. A lot of theoretical questions, such as the expressions of its distribution and moments, remain to be addressed. Motivated by this unsatisfactory situation, in this paper we prove that for samples drawn from bivariate normal populations, the distribution of OSCC is asymptotically equivalent to that of the Pearson's product moment correlation coefficient (PPMCC). We also reveal its close relationships with the other two coefficients, namely, Gini correlation (GC) and Spearman's rho (SR). Monte Carlo simulation results agree with the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel correlation coefficient based on order statistics and rearrangement inequality. The proposed coefficient represents a compromise between the Pearson's linear coefficient and the two rank-based coefficients, namely Spearman's rho and Kendall's tau. Theoretical derivations show that our coefficient possesses the same basic properties as the three classical coefficients. Experimental studies based on four models and six biosignals show that our coefficient performs better than the two rank-based coefficients when measuring linear associations; whereas it is well able to detect monotone nonlinear associations like the two rank-based coefficients. Extensive statistical analyses also suggest that our new coefficient has superior anti-noise robustness, small biasedness, high sensitivity to changes in association, accurate time-delay detection ability, fast computational speed, and robustness under monotone nonlinear transformations. [ABSTRACT FROM AUTHOR]

In this correspondence, we focus on studying the problem of initial condition estimation for chaotic signals within the coupled map lattice (CML) systems. To investigate the effectiveness of a CML initial condition estimation method with different maps and coupling coefficients, the convergence and divergence properties of the inverse CML systems are analyzed. An inverse largest Lyapunov exponent (ILLE) is proposed to investigate the strength of convergence and divergence in the inverse CML systems, and it can determine if the CML initial condition estimation method is effective. Computer simulations are included to verify the relationship between the effectiveness of the CML initial condition estimation method and its corresponding ILLE. [ABSTRACT FROM PUBLISHER]