Letter to the Editor: Zhang, J. (2021), “The Mean Relative Entropy: An Invariant Measure of Estimation Error,” The American Statistician, 75, 117-123:comment by Vos and Wu

To estimate the impact of climate change on our society we need to use climate projections based on numerical models. These models make it possible to assess the effects on climate of the increase in greenhouse gases (GHG) as well as natural variability. We know that the global average temperature will increase and that the occurrence, intensity and spatio-temporal distribution of extreme precipitations will change. These extreme weather events cause droughts, floods and other natural disasters that have significant consequences on our life and environment. Precipitation is a key variable in adapting to climate change.&#160;This study focuses on the ClimEx large ensemble, a set of 50 independent simulations created to study the effect of climate change and natural variability on the water network in Quebec. This dataset consists of simulations produced using the Canadian Regional Climate Model version 5 (CRCM5) at 12 km of resolution driven by simulations from the second generation Canadian Earth System Model (CanESM2) global model at 310 km of resolution.&#160;The aim of the project is to evaluate the performance of the ClimEx ensemble in simulating the daily cycle and representing extreme values.&#160; To get there, 30 years of hourly time series for precipitation and 3 hourly for temperature are analyzed. The simulations are compared with the values from the simulation of CRCM5 driven by ERA-Interim reanalysis, the ERA5 reanalysis and Environment and Climate Change Canada (ECCC) stations. An evaluation of the sensitivity of different statistics to the number of members is also performed.&#160;The daily cycle of precipitation from ClimEx shows mainly non-significant correlations with the other datasets and its amplitude is less than the observation datas from ECCC stations. For temperature, the correlation is strong and the amplitude of the cycle is similar to observations. ClimEx provides a fairly good representation of the 95, 97, 99th quantiles for precipitation. For temperature it represents a good distribution of quantiles but with a warm bias in southern Quebec. For precipitation hourly maximum, ClimEx shows values 10 times higher than ERA5.&#160; For temperature, minimum and maximum values may exceed the ERA5 limit by up to 20&#176;C. For precipitation, the minimum number of members for the estimation of the 95 and 99thquantiles and the mean cycle is between 15 and 50 for an estimation error of less than 5%. For the 95, 99th quantiles of temperature, the minimum number of members is between 1 and 17 and for the mean cycle 1 to 2 members are necessary to obtain an estimation error of less than 0.5&#176;C.

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Sample size for postharvest quality traits of ‘Palmer’ mangoes

Revista Brasileira de Fruticultura ◽

10.1590/0100-29452021014 ◽

2021 ◽

Vol 43 (5) ◽

Author(s):

João Claudio Vilvert ◽

Sérgio Tonetto de Freitas ◽

Maria Aparecida Rodrigues Ferreira ◽

Eleonora Barbosa Santiago da Costa ◽

Edna Maria Mendes Aroucha

Keyword(s):

Sample Size ◽

Estimation Error ◽

Titratable Acidity ◽

Soluble Solids ◽

Postharvest Quality ◽

Maturity Stage ◽

Transverse Diameter ◽

Quality Traits ◽

Growing Seasons ◽

The Mean

Abstract The objective of this study was to determine the most efficient sample size required to estimate the mean of postharvest quality traits of ‘Palmer’ mangoes harvested in two growing seasons. A total of 50 mangoes were harvested at maturity stage 2, in winter (June 2020) and spring (October 2020), and evaluated for weight, length, ventral and transverse diameter, skin and pulp L*, C* and hº, dry matter, firmness, soluble solids (SS), titratable acidity (TA) and the SS/TA ratio. According to the results, the coefficient of variation (CV) of fruit quality traits ranged from 2.1% to 18.1%. The highest CV in both harvests was observed for the SS/TA ratio, while the lowest was reported for pulp hº. In order to estimate the mean of physicochemical traits of ‘Palmer’ mangoes, 12 fruits are needed in the winter and 14 in the spring, considering an estimation error of 10% and a confidence interval of 95%. TA and the SS/TA ratio required the highest sample size, while L* and hº required the lowest sample size. In conclusion, the variability was different among physicochemical traits and seasons, implying that different sample sizes are required to estimate the mean of different quality traits in different growing seasons.

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Minimax Robust Optimal Estimation Fusion for Distributed Multisensor Systems with a Relative Entropy Uncertainty

Mathematical Problems in Engineering ◽

10.1155/2014/910971 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6

Author(s):

Hua Li ◽

Jie Zhou

Keyword(s):

Robust Estimation ◽

Relative Entropy ◽

Estimation Error ◽

Optimal Estimation ◽

Minimum Variance ◽

Estimation Errors ◽

Multisensor Systems ◽

Error Covariance ◽

Local Estimation ◽

Estimation Fusion

This paper considers the robust estimation fusion problem for distributed multisensor systems with uncertain correlations of local estimation errors. For an uncertain class characterized by the Kullback-Leibler (KL) divergence from the actual model to nominal model of local estimation error covariance, the robust estimation fusion problem is formulated to find a linear minimum variance unbiased estimator for the least favorable model. It is proved that the optimal fuser under nominal correlation model is robust while the estimation error has a relative entropy uncertainty.

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Volume-dependent overestimation of spontaneous intracerebral hematoma volume by the ABC/2 formula

Acta Radiologica ◽

10.1080/02841850802647039 ◽

2009 ◽

Vol 50 (3) ◽

pp. 306-311 ◽

Cited By ~ 31

Author(s):

Chih-Wei Wang ◽

Chun-Jung Juan ◽

Yi-Jui Liu ◽

Hsian-He Hsu ◽

Hua-Shan Liu ◽

...

Keyword(s):

Estimation Error ◽

Positive Association ◽

Volumetric Analysis ◽

Intracerebral Hematoma ◽

Computer Assisted ◽

Hematoma Volume ◽

Computed Tomography Scans ◽

Group 3 ◽

The Mean ◽

Group 2

Background: Although the ABC/2 formula has been widely used to estimate the volume of intracerebral hematoma (ICH), the formula tends to overestimate hematoma volume. The volume-related imprecision of the ABC/2 formula has not been documented quantitatively. Purpose: To investigate the volume-dependent overestimation of the ABC/2 formula by comparing it with computer-assisted volumetric analysis (CAVA). Material and Methods: Forty patients who had suffered spontaneous ICH and who had undergone non-enhanced brain computed tomography scans were enrolled in this study. The ICH volume was estimated based on the ABC/2 formula and also calculated by CAVA. Based on the ICH volume calculated by the CAVA method, the patients were divided into three groups: group 1 consisted of 17 patients with an ICH volume of less than 20 ml; group 2 comprised 13 patients with an ICH volume of 20 to 40 ml; and group 3 was composed of 10 patients with an ICH volume larger than 40 ml. Results: The mean estimated hematoma volume was 43.6 ml when using the ABC/2 formula, compared with 33.8 ml when using the CAVA method. The mean estimated difference was 1.3 ml, 4.4 ml, and 31.4 ml for groups 1, 2, and 3, respectively, corresponding to an estimation error of 9.9%, 16.7%, and 37.1% by the ABC/2 formula ( P<0.05). Conclusion: The ABC/2 formula significantly overestimates the volume of ICH. A positive association between the estimation error and the volume of ICH is demonstrated.

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Mutual information, relative entropy and estimation error in semi-martingale channels

2016 IEEE International Symposium on Information Theory (ISIT) ◽

10.1109/isit.2016.7541808 ◽

2016 ◽

Cited By ~ 1

Author(s):

Jiantao Jiao ◽

Kartik Venkat ◽

Tsachy Weissman

Keyword(s):

Mutual Information ◽

Relative Entropy ◽

Estimation Error

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Application of the Mean-Variance Theory and Resampling Technique for the Italian Energy Portfolio Settlement

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.869-870.581 ◽

2013 ◽

Vol 869-870 ◽

pp. 581-592

Author(s):

Mauro Arnesano ◽

Antonio Paolo Carlucci ◽

Giovanni D'Oria ◽

Alessio Guadalupi ◽

Domenico Laforgia

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Estimation Error ◽

Efficient Frontier ◽

Energy Generation ◽

Energy System ◽

Estimation Errors ◽

Energy Mix ◽

The Mean ◽

Mean Variance

The energy planning based on Mean - Variance theory, guides the investors in investment decisions, trying to maximize the return and minimize the risk of investment. However, this theory is based on strong hypotheses and, in addition, input data are often affected by estimation errors. Moreover, this theory determines poor diversification increasing return and risk of the portfolio, and strong variability of the outputs when inputs are varied.In the first part of the paper, the Mean - Variance theory was applied to the energy generation in Italy; in particular, the analysis was on the actual energy mix, but also assuming the use of nuclear technology and taking into account verisimilar improvement, of technologies in the future.On the other hand, in the second part of the paper, a methodology has been applied in order to limit the problems of Mean-Variance theory applied to the energy mix settlement. In particular, the input variables have been calculated using Monte Carlo simulation, in order to reduce the estimation error, and the Resampled EfficiencyTMtechnique has been applied in order to calculate the resulting new “average” efficient frontier. This methodology has been applied either not limiting or limiting the minimum and maximum percentage for every energy generation technology, in order to simulate constraints due, for example, to the technological characteristics of the plant, the availability of the sources and eventually to norms, to the territorial characteristics and to the socio-political choices. The application of Mean - Variance theory allowed to obtain energy portfolio, alternative to the actual, characterized by higher values of expected returns an lower values of risk.It was also shown that the application of the Resampled EfficiencyTMtechnique with data originated with the Monte Carlo simulation effectively tackles the problems of Mean - Variance theory; in this way, the decision maker is helped in making decisions in the energy system policy and development.Thanks to this approach, applied in particular to the Italian energy contest, it was also possible to evaluate the effectiveness of the introduced modifications to the Italian actual energy mix to achieve the 2020 European Energy Directive targets in particular concerning the reduction of CO2levels.

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Kernel Risk-Sensitive Mean p-Power Error Algorithms for Robust Learning

Entropy ◽

10.3390/e21060588 ◽

2019 ◽

Vol 21 (6) ◽

pp. 588 ◽

Cited By ~ 1

Author(s):

Tao Zhang ◽

Shiyuan Wang ◽

Haonan Zhang ◽

Kui Xiong ◽

Lin Wang

Keyword(s):

Similarity Measure ◽

Adaptive Filters ◽

Reproducing Kernel ◽

Reproducing Kernel Hilbert Space ◽

Estimation Error ◽

Network Size ◽

Recursive Least Squares ◽

Robust Learning ◽

Risk Sensitive ◽

The Mean

As a nonlinear similarity measure defined in the reproducing kernel Hilbert space (RKHS), the correntropic loss (C-Loss) has been widely applied in robust learning and signal processing. However, the highly non-convex nature of C-Loss results in performance degradation. To address this issue, a convex kernel risk-sensitive loss (KRL) is proposed to measure the similarity in RKHS, which is the risk-sensitive loss defined as the expectation of an exponential function of the squared estimation error. In this paper, a novel nonlinear similarity measure, namely kernel risk-sensitive mean p-power error (KRP), is proposed by combining the mean p-power error into the KRL, which is a generalization of the KRL measure. The KRP with p = 2 reduces to the KRL, and can outperform the KRL when an appropriate p is configured in robust learning. Some properties of KRP are presented for discussion. To improve the robustness of the kernel recursive least squares algorithm (KRLS) and reduce its network size, two robust recursive kernel adaptive filters, namely recursive minimum kernel risk-sensitive mean p-power error algorithm (RMKRP) and its quantized RMKRP (QRMKRP), are proposed in the RKHS under the minimum kernel risk-sensitive mean p-power error (MKRP) criterion, respectively. Monte Carlo simulations are conducted to confirm the superiorities of the proposed RMKRP and its quantized version.

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