scholarly journals Contour Map of Estimation Error for Expected Shortfall

2015 ◽  
Author(s):  
Imre Kondor ◽  
Fabio Caccioli ◽  
Gabor Papp ◽  
Matteo Marsili
Keyword(s):  
Estimation Error ◽  
Expected Shortfall ◽  
Contour Map

scholarly journals Portfolio optimization under Expected Shortfall: contour maps of estimation error

2017 ◽  
Vol 18 (8) ◽  
pp. 1295-1313 ◽  
Author(s):  
Fabio Caccioli ◽  
Imre Kondor ◽  
Gábor Papp
Keyword(s):  
Portfolio Optimization ◽  
Estimation Error ◽  
Expected Shortfall ◽  
Contour Maps

scholarly journals Optimizing Expected Shortfall under an ℓ1 Constraint—An Analytic Approach

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 523
Author(s):  
Gábor Papp ◽  
Imre Kondor ◽  
Fabio Caccioli
Keyword(s):  
Statistical Physics ◽  
Risk Measure ◽  
Estimation Error ◽  
Random Systems ◽  
Expected Shortfall ◽  
Critical Ratio ◽  
Out Of Sample ◽  
High Volatility ◽  
High Quantile ◽  
Average Loss

Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical ratio r=N/T, where N is the number of different assets in the portfolio, and T is the length of the available time series. The critical ratio depends on the confidence level α, which means we have a line of critical points on the α−r plane. The large fluctuations in the estimation of ES can be attenuated by the application of regularizers. In this paper, we calculate ES analytically under an ℓ1 regularizer by the method of replicas borrowed from the statistical physics of random systems. The ban on short selling, i.e., a constraint rendering all the portfolio weights non-negative, is a special case of an asymmetric ℓ1 regularizer. Results are presented for the out-of-sample and the in-sample estimator of the regularized ES, the estimation error, the distribution of the optimal portfolio weights, and the density of the assets eliminated from the portfolio by the regularizer. It is shown that the no-short constraint acts as a high volatility cutoff, in the sense that it sets the weights of the high volatility elements to zero with higher probability than those of the low volatility items. This cutoff renormalizes the aspect ratio r=N/T, thereby extending the range of the feasibility of optimization. We find that there is a nontrivial mapping between the regularized and unregularized problems, corresponding to a renormalization of the order parameters.

Photographic Equidensitometry of High Voltage Electron Images of Thick Noncrystalline Materials

1972 ◽  
Vol 30 ◽  
pp. 594-595
Author(s):  
Keinosuke Kobayashi
Keyword(s):  
High Voltage ◽  
Linear Response ◽  
Thickness Distribution ◽  
Contour Map ◽  
Mass Thickness ◽  
Voltage Electron ◽  
High Voltage Electron ◽  
Homogeneous Particle ◽  
Photographic Emulsions ◽  
Logarithmic Relation

Equidensitometry as developed by E. Lau and W. Krug has been little used in the analysis of ordinary electron photomicrographs, yet its application to the high voltage electron images proves merits of this procedure. Proper sets (families) of equidensities as shown in the next page are able to reveal the contour map of mass thickness distribution in thick noncrystalline specimens. The change in density of the electron micrograph is directly related to the mass thickness of corresponding area in the specimen, because of the linear response of photographic emulsions to electrons and the logarithmic relation between electron opacity and mass thickness of amorphous object.This linearity is verified by equidensitometry of a spherical solid object as shown in Fig. 1a. The object is a large (1 μ) homogeneous particle of polystyrene. Fig. 1b is a composite print of three equidensities of the 1st order prepared from Fig. 1a.

Temporal Prediction Errors Affect Short-Term Memory Scanning Response Time

2016 ◽  
Vol 63 (6) ◽  
pp. 333-342
Author(s):  
Roberto Limongi ◽  
Angélica M. Silva
Keyword(s):  
Response Time ◽  
Short Term Memory ◽  
Estimation Error ◽  
Predictive Coding ◽  
Time Estimation ◽  
Prediction Errors ◽  
Memory Scanning ◽  
Short Term ◽  
Term Memory ◽  
Temporal Prediction

Abstract. The Sternberg short-term memory scanning task has been used to unveil cognitive operations involved in time perception. Participants produce time intervals during the task, and the researcher explores how task performance affects interval production – where time estimation error is the dependent variable of interest. The perspective of predictive behavior regards time estimation error as a temporal prediction error (PE), an independent variable that controls cognition, behavior, and learning. Based on this perspective, we investigated whether temporal PEs affect short-term memory scanning. Participants performed temporal predictions while they maintained information in memory. Model inference revealed that PEs affected memory scanning response time independently of the memory-set size effect. We discuss the results within the context of formal and mechanistic models of short-term memory scanning and predictive coding, a Bayes-based theory of brain function. We state the hypothesis that our finding could be associated with weak frontostriatal connections and weak striatal activity.

Influence of Channel Estimation Error on MIMO Multiplexing Using Precoding in Downlink OFDM Radio Access

2009 ◽  
Vol E92-B (5) ◽  
pp. 1553-1562
Author(s):  
Takashi ISOGAI ◽  
Mamoru SAWAHASHI ◽  
Hidekazu TAOKA ◽  
Kenichi HIGUCHI
Keyword(s):  
Channel Estimation ◽  
Estimation Error ◽  
Channel Estimation Error ◽  
Radio Access
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