Estimators based on sample quantiles using (h, φ)-entropy measures

Menéndez, M.; Pardo, J. A.; Pardo, M. C.

doi:10.1016/s0893-9659(98)00064-0

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…These authors based their proposal in the well-known Shannon entropy. In the past there has been an extensive work on generalized entropies [30][31][32][36][37][38][39]. We focus on the Havrda-Charvat entropy, which reduces to the Shannon case if the parameter is set to one, to extend that surrogacy measure.…”

Section: Discussionmentioning

confidence: 99%

“…The optimal choice of α remains a research question. Additional research can consider other ITMA, such as divergence measures [ 36 ], taking into account that the mutual information is equal to the Kullback divergence, or measures of unilateral dependency as that defined by Andonie et al [ 37 ] based on the informational energy [ 39 ] or surrogacy for testing of variances [ 38 ].…”

Section: Discussionmentioning

confidence: 99%

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Evaluation of Surrogate Endpoints Using Information-Theoretic Measure of Association Based on Havrda and Charvat Entropy

et al. 2022

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Surrogate endpoints have been used to assess the efficacy of a treatment and can potentially reduce the duration and/or number of required patients for clinical trials. Using information theory, Alonso et al. (2007) proposed a unified framework based on Shannon entropy, a new definition of surrogacy that departed from the hypothesis testing framework. In this paper, a new family of surrogacy measures under Havrda and Charvat (H-C) entropy is derived which contains Alonso’s definition as a particular case. Furthermore, we extend our approach to a new model based on the information-theoretic measure of association for a longitudinally collected continuous surrogate endpoint for a binary clinical endpoint of a clinical trial using H-C entropy. The new model is illustrated through the analysis of data from a completed clinical trial. It demonstrates advantages of H-C entropy-based surrogacy measures in the evaluation of scheduling longitudinal biomarker visits for a phase 2 randomized controlled clinical trial for treatment of multiple sclerosis.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Evaluation of Surrogate Endpoints Using Information-Theoretic Measure of Association Based on Havrda and Charvat Entropy

et al. 2022

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“…Numerical examples have indicated that the MEE criterion could achieve a better error distribution, especially for higher-order statistics in the adaptive system training [3]. In the literature of statistical information theory, there are many other important entropy measures different from Shannon's and Renyi's definitions [12][13][14]. Similar to the MMSE criterion, Shannon's entropy is also not always the optimum entropy criterion.…”

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confidence: 99%

Stochastic Gradient Algorithm Under (h,φ)-Entropy Criterion

Chen

et al. 2007

Circuits Syst Signal Process

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Motivated by the work of Erdogmus and Principe, we use the error (h, φ)-entropy as the supervised adaptation criterion. Several properties of the (h, φ)-entropy criterion and the connections with traditional error criteria are investigated. By a kernel estimate approach, we obtain the nonparametric estimator of the instantaneous (h, φ)-entropy. Then, we develop the general stochastic information gradient algorithm, and derive the approximate upper bound for the step size in the adaptive linear neuron training. Moreover, the (h, φ) pair are optimized to improve the performance of the proposed algorithm. For the finite impulse response identification with white Gaussian input and noise, the exact optimum φ function is derived. Finally, simulation experiments verify the results and demonstrate the noticeable performance improvement that may be achieved by the optimum (h, φ)-entropy criterion.

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