Search results for " logarithmic scoring rule"

showing 4 items of 4 documents

Assessing fat-tailed sequential forecast distributions for the Dow-Jones index with logarithmic scoring rules

2007

We use the logarithmic scoring rule for distributions to assess a variety of fat-tailed sequential forecasting distributions for the Dow-Jones industrial stock index from 1980 to the present. The methodology applies Bruno de Finetti''s contributions to understanding how to compare the quality of different coherent forecasting distributions for the same sequence of observations, using proper scoring rules. Four different forms of forecasting distributions are compared: a mixture Normal, a mixture of convex combinations of three Normal distributions, a mixture exponential power distribution, and a mixture of a convex combination of three exponential power distributions. The mixture linear com…

Dow-Jones index exponential power distributions fat tails logarithmic scoring rule mixture distributions partial exchangeability proper scoring rules subjective probability subjectivist statistical methods.
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The Duality of Entropy/Extropy, and Completion of the Kullback Information Complex

2018

The refinement axiom for entropy has been provocative in providing foundations of information theory, recognised as thoughtworthy in the writings of both Shannon and Jaynes. A resolution to their concerns has been provided recently by the discovery that the entropy measure of a probability distribution has a dual measure, a complementary companion designated as &ldquo

Kullback–Leibler divergenceSettore MAT/06 - Probabilita' E Statistica MatematicaLogarithmGeneral Physics and Astronomylcsh:Astrophysics02 engineering and technologyBregman divergenceMathematical proofInformation theory01 natural sciencesArticle010104 statistics & probabilityFermi–Dirac entropyKullback symmetric divergencelcsh:QB460-4660202 electrical engineering electronic engineering information engineeringEntropy (information theory)0101 mathematicslcsh:Sciencerelative entropy/extropyAxiomMathematics020206 networking & telecommunicationslcsh:QC1-999total logarithmic scoring ruleProbability distributiondualityPareto optimal exchangelcsh:QprevisionextropySettore SECS-S/01 - StatisticaentropyMathematical economicslcsh:PhysicsEntropy
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Sequentially Forecasting Economic Indices Using Mixture Linear Combinations of EP Distributions

2021

This article displays an application of the statistical method moti- vated by Bruno de Finetti's operational subjective theory of probability. We use exchangeable forecasting distributions based on mixtures of linear com- binations of exponential power (EP) distributions to forecast the sequence of daily rates of return from the Dow-Jones index of stock prices over a 20 year period. The operational subjective statistical method for comparing distributions is quite different from that commonly used in data analysis, because it rejects the basic tenets underlying the practice of hypothesis test- ing. In its place, proper scoring rules for forecast distributions are used to assess the values o…

Settore MAT/06 - Probabilita' E Statistica MatematicaLogarithmDow-Jones index exponential power distributions fat tails logarithmic scoring rule mixture distributions partial exchangeability proper scoring rules subjective probability subjectivist statistical methods.Scoring ruleStatistical parameterExponential functionNormal distributionSettore SECS-S/06 -Metodi Mat. dell'Economia e d. Scienze Attuariali e Finanz.StatisticsEconometricsSettore SECS-S/01 - StatisticaLinear combinationMathematicsStatistical hypothesis testingJournal of Data Science
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SCORING ALTERNATIVE FORECAST DISTRIBUTIONS: COMPLETING THE KULLBACK DISTANCE COMPLEX

2018

We develop two surprising new results regarding the use of proper scoring rules for evaluating the predictive quality of two alternative sequential forecast distributions. Both of the proponents prefer to be awarded a score derived from the other's distribution rather than a score awarded on the basis of their own. A Pareto optimal exchange of their scoring outcomes provides the basis for a comparison of forecast quality that is preferred by both forecasters, and also evades a feature of arbitrariness inherent in using the forecasters' own achieved scores. The well-known Kullback divergence, used as a measure of information, is evaluated via the entropies in the two forecast distributions a…

Settore MAT/06 - Probabilita' E Statistica MatematicaProbability (math.PR)Mathematics - Statistics TheoryStatistics Theory (math.ST)PARETO OPTIMAL EXCHANGETOTAL LOGARITHMIC SCORING RULEKULLBACK SYMMETRIC DIVERGENCEPREVISIONENTROPY/EXTROPYSettore SECS-S/06 -Metodi Mat. dell'Economia e d. Scienze Attuariali e Finanz.FOS: MathematicsMathematics - ProbabilityCROSS ENTROPYBREGMAN DIVERGENCE
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