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Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative entropy, just as Sobol sensitivity analysis does not have negative variance. Entropy is similar to variance but does not have the same properties. An alternative sensitivity measure based on the approximation of the differential entropy using dome-shaped functionals with non-negative values is proposed in the article. Case studies have shown that new sensitivity measures lead to a rational structure of sensitivity indices with a significantly lower proportion of higher-order sensitivity indices compared to other types of distributional sensitivity analysis. In terms of the concept of sensitivity analysis, a decrease in variance to zero means a transition from the differential to discrete entropy. The form of this transition is an open question, which can be studied using other scientific disciplines. The search for new functionals for distributional sensitivity analysis is not closed, and other suitable sensitivity measures may be found., Diferenciální entropie může být záporná, zatímco diskrétní entropie je vždy nezáporná. Tento článek ukazuje, že záporná entropie je významnou chybou, když je entropie použita jako citlivostní míra v globální citlivostní analýze. Globální citlivostní analýza založená na diferenciální entropii nemůže mít negativní entropii, stejně jako Sobolova citlivostní analýza nemá negativní rozptyl. Entropie je podobná rozptylu, ale nemá stejné vlastnosti. V článku je navrženo alternativní měření citlivosti založené na aproximaci diferenciální entropie pomocí kopulovitých funkcionálů s nezápornými hodnotami. Případové studie ukázaly, že nová měření citlivosti vedou k racionální struktuře indexů citlivosti s výrazně nižším podílem indexů citlivosti vyššího řádu ve srovnání s jinými typy distribučních citlivostních analýz. Z hlediska konceptu citlivostní analýzy znamená pokles rozptylu na nulu přechod od diferenciální k diskrétní entropii. Forma tohoto přechodu je otevřenou otázkou, kterou lze studovat pomocí jiných vědních oborů. Hledání nových funkcionálů pro distribuční analýzu citlivosti není uzavřeno a lze nalézt další vhodná opatření pro citlivost.

Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative entropy, just as Sobol sensitivity analysis does not have negative variance. Entropy is similar to variance but does not have the same properties. An alternative sensitivity measure based on the approximation of the differential entropy using dome-shaped functionals with non-negative values is proposed in the article. Case studies have shown that new sensitivity measures lead to a rational structure of sensitivity indices with a significantly lower proportion of higher-order sensitivity indices compared to other types of distributional sensitivity analysis. In terms of the concept of sensitivity analysis, a decrease in variance to zero means a transition from the differential to discrete entropy. The form of this transition is an open question, which can be studied using other scientific disciplines. The search for new functionals for distributional sensitivity analysis is not closed, and other suitable sensitivity measures may be found., Diferenciální entropie může být záporná, zatímco diskrétní entropie je vždy nezáporná. Tento článek ukazuje, že záporná entropie je významnou chybou, když je entropie použita jako citlivostní míra v globální citlivostní analýze. Globální citlivostní analýza založená na diferenciální entropii nemůže mít negativní entropii, stejně jako Sobolova citlivostní analýza nemá negativní rozptyl. Entropie je podobná rozptylu, ale nemá stejné vlastnosti. V článku je navrženo alternativní měření citlivosti založené na aproximaci diferenciální entropie pomocí kopulovitých funkcionálů s nezápornými hodnotami. Případové studie ukázaly, že nová měření citlivosti vedou k racionální struktuře indexů citlivosti s výrazně nižším podílem indexů citlivosti vyššího řádu ve srovnání s jinými typy distribučních citlivostních analýz. Z hlediska konceptu citlivostní analýzy znamená pokles rozptylu na nulu přechod od diferenciální k diskrétní entropii. Forma tohoto přechodu je otevřenou otázkou, kterou lze studovat pomocí jiných vědních oborů. Hledání nových funkcionálů pro distribuční analýzu citlivosti není uzavřeno a lze nalézt další vhodná opatření pro citlivost.

Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative entropy, just as Sobol sensitivity analysis does not have negative variance. Entropy is similar to variance but does not have the same properties. An alternative sensitivity measure based on the approximation of the differential entropy using dome-shaped functionals with non-negative values is proposed in the article. Case studies have shown that new sensitivity measures lead to a rational structure of sensitivity indices with a significantly lower proportion of higher-order sensitivity indices compared to other types of distributional sensitivity analysis. In terms of the concept of sensitivity analysis, a decrease in variance to zero means a transition from the differential to discrete entropy. The form of this transition is an open question, which can be studied using other scientific disciplines. The search for new functionals for distributional sensitivity analysis is not closed, and other suitable sensitivity measures may be found., Diferenciální entropie může být záporná, zatímco diskrétní entropie je vždy nezáporná. Tento článek ukazuje, že záporná entropie je významnou chybou, když je entropie použita jako citlivostní míra v globální citlivostní analýze. Globální citlivostní analýza založená na diferenciální entropii nemůže mít negativní entropii, stejně jako Sobolova citlivostní analýza nemá negativní rozptyl. Entropie je podobná rozptylu, ale nemá stejné vlastnosti. V článku je navrženo alternativní měření citlivosti založené na aproximaci diferenciální entropie pomocí kopulovitých funkcionálů s nezápornými hodnotami. Případové studie ukázaly, že nová měření citlivosti vedou k racionální struktuře indexů citlivosti s výrazně nižším podílem indexů citlivosti vyššího řádu ve srovnání s jinými typy distribučních citlivostních analýz. Z hlediska konceptu citlivostní analýzy znamená pokles rozptylu na nulu přechod od diferenciální k diskrétní entropii. Forma tohoto přechodu je otevřenou otázkou, kterou lze studovat pomocí jiných vědních oborů. Hledání nových funkcionálů pro distribuční analýzu citlivosti není uzavřeno a lze nalézt další vhodná opatření pro citlivost.

Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative entropy, just as Sobol sensitivity analysis does not have negative variance. Entropy is similar to variance but does not have the same properties. An alternative sensitivity measure based on the approximation of the differential entropy using dome-shaped functionals with non-negative values is proposed in the article. Case studies have shown that new sensitivity measures lead to a rational structure of sensitivity indices with a significantly lower proportion of higher-order sensitivity indices compared to other types of distributional sensitivity analysis. In terms of the concept of sensitivity analysis, a decrease in variance to zero means a transition from the differential to discrete entropy. The form of this transition is an open question, which can be studied using other scientific disciplines. The search for new functionals for distributional sensitivity analysis is not closed, and other suitable sensitivity measures may be found., Diferenciální entropie může být záporná, zatímco diskrétní entropie je vždy nezáporná. Tento článek ukazuje, že záporná entropie je významnou chybou, když je entropie použita jako citlivostní míra v globální citlivostní analýze. Globální citlivostní analýza založená na diferenciální entropii nemůže mít negativní entropii, stejně jako Sobolova citlivostní analýza nemá negativní rozptyl. Entropie je podobná rozptylu, ale nemá stejné vlastnosti. V článku je navrženo alternativní měření citlivosti založené na aproximaci diferenciální entropie pomocí kopulovitých funkcionálů s nezápornými hodnotami. Případové studie ukázaly, že nová měření citlivosti vedou k racionální struktuře indexů citlivosti s výrazně nižším podílem indexů citlivosti vyššího řádu ve srovnání s jinými typy distribučních citlivostních analýz. Z hlediska konceptu citlivostní analýzy znamená pokles rozptylu na nulu přechod od diferenciální k diskrétní entropii. Forma tohoto přechodu je otevřenou otázkou, kterou lze studovat pomocí jiných vědních oborů. Hledání nových funkcionálů pro distribuční analýzu citlivosti není uzavřeno a lze nalézt další vhodná opatření pro citlivost.

Identifying people who are at risk of fall during walking is crucial. The objective of this thesis is to comprehensively evaluate the application of two selected entropy measures, sample entropy (SampEn) and quantized dynamical entropy (QDE), as biomarkers of increased fall risk when applied to whole gait signals. SampEn is the most used entropy measure in human gait studies and QDE has the robustness of SampEn to noise but offers a superior computational performance. The first study further investigates the viability of SampEn and QDE along with choosing the signal which best discriminates between young healthy adults and elderly fallers as well as between walk only and dual-task walking condition. The results suggest that, amongst the five different signals representing trunk motion, leg motion, and the center of pressure of feet displacement, the center of pressure in the mediolateral direction (ML COP-D) is the best signal. The second study establishes the sensitivity of the SampEn and QDE of the ML COP-D signal to two preprocessing methods and to variant values of template size, tolerance size, and sampling rate. The results suggest that SampEn and QDE benefit from a relative consistency across variant parameter values, showing a significant increase from walk only to dual-task walking condition, especially when signals are low-pass filtered. Finally, the correlation of SampEn and QDE with two other families of gait measures (i.e., variability measures and the short-term largest Lyapunov exponent [LLE] measure), which have been used for gait stability assessment, is investigated. Two difficulty levels for the secondary visuomotor cognitive games are used. The results show that all gait measures increase due to dual-tasking, except for the short-term LLE which increases significantly only during the easy game. Additionally, these measures are not sensitive to the degree of difficulty of the secondary tasks. This is along with a poorer task performance when parti

Identifying people who are at risk of fall during walking is crucial. The objective of this thesis is to comprehensively evaluate the application of two selected entropy measures, sample entropy (SampEn) and quantized dynamical entropy (QDE), as biomarkers of increased fall risk when applied to whole gait signals. SampEn is the most used entropy measure in human gait studies and QDE has the robustness of SampEn to noise but offers a superior computational performance. The first study further investigates the viability of SampEn and QDE along with choosing the signal which best discriminates between young healthy adults and elderly fallers as well as between walk only and dual-task walking condition. The results suggest that, amongst the five different signals representing trunk motion, leg motion, and the center of pressure of feet displacement, the center of pressure in the mediolateral direction (ML COP-D) is the best signal. The second study establishes the sensitivity of the SampEn and QDE of the ML COP-D signal to two preprocessing methods and to variant values of template size, tolerance size, and sampling rate. The results suggest that SampEn and QDE benefit from a relative consistency across variant parameter values, showing a significant increase from walk only to dual-task walking condition, especially when signals are low-pass filtered. Finally, the correlation of SampEn and QDE with two other families of gait measures (i.e., variability measures and the short-term largest Lyapunov exponent [LLE] measure), which have been used for gait stability assessment, is investigated. Two difficulty levels for the secondary visuomotor cognitive games are used. The results show that all gait measures increase due to dual-tasking, except for the short-term LLE which increases significantly only during the easy game. Additionally, these measures are not sensitive to the degree of difficulty of the secondary tasks. This is along with a poorer task performance when parti

[EN] Optimal defibrillation timing guided by ventricular fibrillation (VF) waveform analysis would contribute to improved survival of out-of-hospital cardiac arrest (OHCA) patients by minimizing myocardial damage caused by futile defibrillation shocks and minimizing interruptions to cardiopulmonary resuscitation. Recently, fuzzy entropy (FuzzyEn) tailored to jointly measure VF amplitude and regularity has been shown to be an efficient defibrillation success predictor. In this study, 734 shocks from 296 OHCA patients (50 survivors) were analyzed, and the embedding dimension (m) and matching tolerance (r) for FuzzyEn and sample entropy (SampEn) were adjusted to predict defibrillation success and patient survival. Entropies were significantly larger in successful shocks and in survivors, and when compared to the available methods, FuzzyEn presented the best prediction results, marginally outperforming SampEn. The sensitivity and specificity of FuzzyEn were 83.3% and 76.7% when predicting defibrillation success, and 83.7% and 73.5% for patient survival. Sensitivities and specificities were two points above those of the best available methods, and the prediction accuracy was kept even for VF intervals as short as 2s. These results suggest that FuzzyEn and SampEn may be promising tools for optimizing the defibrillation time and predicting patient survival in OHCA patients presenting VF.

[EN] Optimal defibrillation timing guided by ventricular fibrillation (VF) waveform analysis would contribute to improved survival of out-of-hospital cardiac arrest (OHCA) patients by minimizing myocardial damage caused by futile defibrillation shocks and minimizing interruptions to cardiopulmonary resuscitation. Recently, fuzzy entropy (FuzzyEn) tailored to jointly measure VF amplitude and regularity has been shown to be an efficient defibrillation success predictor. In this study, 734 shocks from 296 OHCA patients (50 survivors) were analyzed, and the embedding dimension (m) and matching tolerance (r) for FuzzyEn and sample entropy (SampEn) were adjusted to predict defibrillation success and patient survival. Entropies were significantly larger in successful shocks and in survivors, and when compared to the available methods, FuzzyEn presented the best prediction results, marginally outperforming SampEn. The sensitivity and specificity of FuzzyEn were 83.3% and 76.7% when predicting defibrillation success, and 83.7% and 73.5% for patient survival. Sensitivities and specificities were two points above those of the best available methods, and the prediction accuracy was kept even for VF intervals as short as 2s. These results suggest that FuzzyEn and SampEn may be promising tools for optimizing the defibrillation time and predicting patient survival in OHCA patients presenting VF.

Optimal defibrillation timing guided by ventricular fibrillation (VF) waveform analysis would contribute to improved survival of out-of-hospital cardiac arrest (OHCA) patients by minimizing myocardial damage caused by futile defibrillation shocks and minimizing interruptions to cardiopulmonary resuscitation. Recently, fuzzy entropy (FuzzyEn) tailored to jointly measure VF amplitude and regularity has been shown to be an efficient defibrillation success predictor. In this study, 734 shocks from 296 OHCA patients (50 survivors) were analyzed, and the embedding dimension (m) and matching tolerance (r) for FuzzyEn and sample entropy (SampEn) were adjusted to predict defibrillation success and patient survival. Entropies were significantly larger in successful shocks and in survivors, and when compared to the available methods, FuzzyEn presented the best prediction results, marginally outperforming SampEn. The sensitivity and specificity of FuzzyEn were 83.3% and 76.7% when predicting defibrillation success, and 83.7% and 73.5% for patient survival. Sensitivities and specificities were two points above those of the best available methods, and the prediction accuracy was kept even for VF intervals as short as 2s. These results suggest that FuzzyEn and SampEn may be promising tools for optimizing the defibrillation time and predicting patient survival in OHCA patients presenting VF.

Cerebellar Ataxia (CA) leads to deficiencies in muscle movement and lack of coordination that is often manifested as gait and balance disabilities. Conventional CA clinical assessments are subjective, cumbersome and provide less insight into the functional capabilities of patients. This cross-sectional study investigates the use of wearable inertial sensors strategically positioned on the front-chest and upper-back locations during the Romberg and Trunk tests for objective assessment of human postural balance due to CA. The primary aim of this paper is to quantify the performance of postural stability of 34 patients diagnosed with CA and 22 healthy subjects as controls. Several forms of entropy descriptions were considered to uncover characteristics of movements intrinsic to CA. Indeed, correlation with clinical observation is vital in ascertaining the validity of the inertial measurements in addition to capturing unique features of movements not typically observed by the practicing clinician. Both of these aspects form an integral part of the underlying objective assessment scheme. Uncertainty in the velocity contained a significant level of information with respect to truncal instability and, based on an extensive clustering and discrimination analysis, fuzzy entropy was identified as an effective measure in characterising the underlying disability. Front-chest measurements demonstrated a strong correlation with clinical assessments while the upper-back measurements performed better in classifying the two cohorts, inferring that the standard clinical assessments are relatively influenced by the frontal observations. The Romberg test was confirmed to be an effective test of neurological diagnosis as well as a potential candidate for objective assessment resulting in a significant correlation with the clinical assessments. In contrast, the Trunk test is observed to be relatively less informative.

Optimal defibrillation timing guided by ventricular fibrillation (VF) waveform analysis would contribute to improved survival of out-of-hospital cardiac arrest (OHCA) patients by minimizing myocardial damage caused by futile defibrillation shocks and minimizing interruptions to cardiopulmonary resuscitation. Recently, fuzzy entropy (FuzzyEn) tailored to jointly measure VF amplitude and regularity has been shown to be an efficient defibrillation success predictor. In this study, 734 shocks from 296 OHCA patients (50 survivors) were analyzed, and the embedding dimension (m) and matching tolerance (r) for FuzzyEn and sample entropy (SampEn) were adjusted to predict defibrillation success and patient survival. Entropies were significantly larger in successful shocks and in survivors, and when compared to the available methods, FuzzyEn presented the best prediction results, marginally outperforming SampEn. The sensitivity and specificity of FuzzyEn were 83.3% and 76.7% when predicting defibrillation success, and 83.7% and 73.5% for patient survival. Sensitivities and specificities were two points above those of the best available methods, and the prediction accuracy was kept even for VF intervals as short as 2s. These results suggest that FuzzyEn and SampEn may be promising tools for optimizing the defibrillation time and predicting patient survival in OHCA patients presenting VF.

Optimal defibrillation timing guided by ventricular fibrillation (VF) waveform analysis would contribute to improved survival of out-of-hospital cardiac arrest (OHCA) patients by minimizing myocardial damage caused by futile defibrillation shocks and minimizing interruptions to cardiopulmonary resuscitation. Recently, fuzzy entropy (FuzzyEn) tailored to jointly measure VF amplitude and regularity has been shown to be an efficient defibrillation success predictor. In this study, 734 shocks from 296 OHCA patients (50 survivors) were analyzed, and the embedding dimension (m) and matching tolerance (r) for FuzzyEn and sample entropy (SampEn) were adjusted to predict defibrillation success and patient survival. Entropies were significantly larger in successful shocks and in survivors, and when compared to the available methods, FuzzyEn presented the best prediction results, marginally outperforming SampEn. The sensitivity and specificity of FuzzyEn were 83.3% and 76.7% when predicting defibrillation success, and 83.7% and 73.5% for patient survival. Sensitivities and specificities were two points above those of the best available methods, and the prediction accuracy was kept even for VF intervals as short as 2s. These results suggest that FuzzyEn and SampEn may be promising tools for optimizing the defibrillation time and predicting patient survival in OHCA patients presenting VF.

Optimal defibrillation timing guided by ventricular fibrillation (VF) waveform analysis would contribute to improved survival of out-of-hospital cardiac arrest (OHCA) patients by minimizing myocardial damage caused by futile defibrillation shocks and minimizing interruptions to cardiopulmonary resuscitation. Recently, fuzzy entropy (FuzzyEn) tailored to jointly measure VF amplitude and regularity has been shown to be an efficient defibrillation success predictor. In this study, 734 shocks from 296 OHCA patients (50 survivors) were analyzed, and the embedding dimension (m) and matching tolerance (r) for FuzzyEn and sample entropy (SampEn) were adjusted to predict defibrillation success and patient survival. Entropies were significantly larger in successful shocks and in survivors, and when compared to the available methods, FuzzyEn presented the best prediction results, marginally outperforming SampEn. The sensitivity and specificity of FuzzyEn were 83.3% and 76.7% when predicting defibrillation success, and 83.7% and 73.5% for patient survival. Sensitivities and specificities were two points above those of the best available methods, and the prediction accuracy was kept even for VF intervals as short as 2s. These results suggest that FuzzyEn and SampEn may be promising tools for optimizing the defibrillation time and predicting patient survival in OHCA patients presenting VF.

Prediction of defibrillation success is of vital importance to guide therapy and improve the survival of patients suffering out-of-hospital cardiac arrest (OHCA). Currently, the most efficient methods to predict shock success are based on the analysis of the electrocardiogram (ECG) during ventricular fibrillation (VF), and recent studies suggest the efficacy of waveform indices that characterize the underlying non-linear dynamics of VF. In this study we introduce, adapt and fully characterize six entropy indices for VF shock outcome prediction, based on the classical definitions of entropy to measure the regularity and predictability of a time series. Data from 163 OHCA patients comprising 419 shocks (107 successful) were used, and the performance of the entropy indices was characterized in terms of embedding dimension (m) and matching tolerance (r). Six classical predictors were also assessed as baseline prediction values. The best prediction results were obtained for fuzzy entropy (FuzzEn) with m = 3 and an amplitude-dependent tolerance of r = 80 mu V. This resulted in a balanced sensitivity/specificity of 80.4%/76.9%, which improved by over five points the results obtained for the best classical predictor. These results suggest that a FuzzEn approach for a joint quantification of VF amplitude and its non-linear dynamics may be a promising tool to optimize OHCA treatment.

Prediction of defibrillation success is of vital importance to guide therapy and improve the survival of patients suffering out-of-hospital cardiac arrest (OHCA). Currently, the most efficient methods to predict shock success are based on the analysis of the electrocardiogram (ECG) during ventricular fibrillation (VF), and recent studies suggest the efficacy of waveform indices that characterize the underlying non-linear dynamics of VF. In this study we introduce, adapt and fully characterize six entropy indices for VF shock outcome prediction, based on the classical definitions of entropy to measure the regularity and predictability of a time series. Data from 163 OHCA patients comprising 419 shocks (107 successful) were used, and the performance of the entropy indices was characterized in terms of embedding dimension (m) and matching tolerance (r). Six classical predictors were also assessed as baseline prediction values. The best prediction results were obtained for fuzzy entropy (FuzzEn) with m = 3 and an amplitude-dependent tolerance of r = 80 mu V. This resulted in a balanced sensitivity/specificity of 80.4%/76.9%, which improved by over five points the results obtained for the best classical predictor. These results suggest that a FuzzEn approach for a joint quantification of VF amplitude and its non-linear dynamics may be a promising tool to optimize OHCA treatment.

Prediction of defibrillation success is of vital importance to guide therapy and improve the survival of patients suffering out-of-hospital cardiac arrest (OHCA). Currently, the most efficient methods to predict shock success are based on the analysis of the electrocardiogram (ECG) during ventricular fibrillation (VF), and recent studies suggest the efficacy of waveform indices that characterize the underlying non-linear dynamics of VF. In this study we introduce, adapt and fully characterize six entropy indices for VF shock outcome prediction, based on the classical definitions of entropy to measure the regularity and predictability of a time series. Data from 163 OHCA patients comprising 419 shocks (107 successful) were used, and the performance of the entropy indices was characterized in terms of embedding dimension (m) and matching tolerance (r). Six classical predictors were also assessed as baseline prediction values. The best prediction results were obtained for fuzzy entropy (FuzzEn) with m = 3 and an amplitude-dependent tolerance of r = 80 mu V. This resulted in a balanced sensitivity/specificity of 80.4%/76.9%, which improved by over five points the results obtained for the best classical predictor. These results suggest that a FuzzEn approach for a joint quantification of VF amplitude and its non-linear dynamics may be a promising tool to optimize OHCA treatment.

Networks are systems of point (nodes) with connections among some pairs of nodes measuring the degree of linkage. Networks represent an entire problem domain of many of the most difficult and unsolved mathematical problems. The objective of this effort was to formulate a foundational structure for networks and specifically develop new mathematical metrics for the description of networks in order to usefully describe both the static and dynamic properties of networks. Specifically, these new metrics provide a means of monitoring networks such as internet traffic over time by identifying anomalies, malicious processes, and abnormal network behavior. The criteria used for establishing network metrics were: (a) well-defined mathematically, (b) lossless in the description of a network, (c) hierarchical in providing a sequence of numerical metrics of decreasing importance, (d) intuitive in order to guide the use of the mathematical network expansions and associated metric values, (e) descriptive of the inherent topology of the network and strengths of connectivity, (f) sufficiently fast computationally in order to be dynamically useful as a tool, and (g) ideally distinguishing types of metrics that are: (1) network invariants, (2) variables which have dynamic behavior, and (3) variables which are chaotic or random. Results include: (a) finding network metrics that satisfy these criteria, (b) building the computer software to derive such metrics for general networks, and (c) testing limited internet traffic with this software., Sponsored in part by Defense Advanced Research Projects Agency (DARPA). The original document contains color images.

In this paper, we study some applications of unified (r, s)-entropy measures in Bayesian inference, specially in comparison of experiments. Also, we analize the relation between Blackwell's and Lehmann's approach with the criterion established in this work., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper, we study some applications of unified (r, s)-entropy measures in Bayesian inference, specially in comparison of experiments. Also, we analize the relation between Blackwell's and Lehmann's approach with the criterion established in this work., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub