Search results for "Likelihood principle"

showing 3 items of 3 documents

Completing the logarithmic scoring rule for assessing probability distributions

2012

We propose and motivate an expanded version of the logarithmic score for forecasting distributions, termed the Total Log score. It incorporates the usual logarithmic score, which is recognised as incomplete and has been mistakenly associated with the likelihood principle. The expectation of the Total Log score equals the Negentropy plus the Negextropy of the distribution. We examine both discrete and continuous forms of the scoring rule, and we discuss issues of scaling for scoring assessments. The analysis suggests the dual tracking of the quadratic score along with the usual log score when assessing the qualities of probability distributions. An application to the sequential scoring of f…

Settore MAT/06 - Probabilita' E Statistica MatematicaLogarithmScoring ruleDow-Jones stock indexScoreLikelihood principletotal log scorelogarithmic scoreProbability theoryStatisticsproper scoring ruleEconometricsEntropy (information theory)Probability distributionNegentropyextropyentropySettore SECS-S/01 - StatisticaMathematicsAIP Conference Proceedings
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Maximum likelihood estimation for the exponential power function parameters

1995

This paper addresses the problem of obtaining maximum likelihood estimates for the three parameters of the exponential power function; the information matrix is derived and the covariance matrix is here presented; the regularity conditions which ensure asymptotic normality and efficiency are examined. A numerical investigation is performed for exploring the bias and variance of the maximum likelihood estimates and their dependence on sample size and shape parameter.

Statistics and ProbabilityEstimation theoryRestricted maximum likelihoodMaximum likelihood sequence estimationLikelihood principlesymbols.namesakeEstimation of covariance matricesModeling and SimulationStatisticsExpectation–maximization algorithmsymbolsFisher informationLikelihood functionMathematicsCommunications in Statistics - Simulation and Computation
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Parameter orthogonality and conditional profile likelihood: the exponential power function case

1999

Orthogonality, according to Fisher’s metrics, between the parameters of a probability density function, as well as giving rise to a series of statistical implications, makes it possible to express a function of conditional profile likelihood with better properties than the ordinary profile likelihood function. In the present paper the parameters of exponential power function are made orthogonal and the conditional profile likelihood of the shape parameter p is determined in order to study its properties with reference to p estimation. Moreover, by means of a simulation plan, a comparison is made between the estimates of p obtained from the conditional profile log-likelihood and those obtain…

Statistics and ProbabilityStatisticsApplied mathematicsProbability density functionDensity estimationConditional probability distributionLikelihood functionLikelihood principleConditional varianceShape parameterExponential functionMathematicsCommunications in Statistics - Theory and Methods
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