Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?
Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur Graph Search.
Concept
Maximum spacing estimation
Résumé
In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model. The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution function at neighbouring data points.
The concept underlying the method is based on the probability integral transform, in that a set of independent random samples derived from any random variable should on average be uniformly distributed with respect to the cumulative distribution function of the random variable. The MPS method chooses the parameter values that make the observed data as uniform as possible, according to a specific quantitative measure of uniformity.
One of the most common methods for estimating the parameters of a distribution from data, the method of maximum likelihood (MLE), can break down in various cases, such as involving certain mixtures of continuous distributions. In these cases the method of maximum spacing estimation may be successful.
Apart from its use in pure mathematics and statistics, the trial applications of the method have been reported using data from fields such as hydrology, econometrics, magnetic resonance imaging, and others.
The MSE method was derived independently by Russel Cheng and Nik Amin at the University of Wales Institute of Science and Technology, and Bo Ranneby at the Swedish University of Agricultural Sciences. The authors explained that due to the probability integral transform at the true parameter, the “spacing” between each observation should be uniformly distributed. This would imply that the difference between the values of the cumulative distribution function at consecutive observations should be equal. This is the case that maximizes the geometric mean of such spacings, so solving for the parameters that maximize the geometric mean would achieve the “best” fit as defined this way.
Source officielle
À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.
Cours associés (22)
MATH-413: Statistics for data science
Statistics lies at the foundation of data science, providing a unifying theoretical and methodological backbone for the diverse tasks enountered in this emerging field. This course rigorously develops
MATH-336: Randomization and causation
This course covers formal frameworks for causal inference. We focus on experimental designs, definitions of causal models, interpretation of causal parameters and estimation of causal effects.
FIN-474: Advanced risk management topics
The students learn different financial risk measures and their risk theoretical properties. They learn how to design and implement risk engines, with model estimation, forecast, reporting and validati