Robust measures of scale | EPFL Graph Search

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 GraphSearch.

Découvrez-en plus sur les applications Graph.

In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The most common such robust statistics are the interquartile range (IQR) and the median absolute deviation (MAD). These are contrasted with conventional or non-robust measures of scale, such as sample standard deviation, which are greatly influenced by outliers. These robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency on contaminated data, at the cost of inferior efficiency on clean data from distributions such as the normal distribution. To illustrate robustness, the standard deviation can be made arbitrarily large by increasing exactly one observation (it has a breakdown point of 0, as it can be contaminated by a single point), a defect that is not shared by robust statistics. One of the most common robust measures of scale is the interquartile range (IQR), the difference between the 75th percentile and the 25th percentile of a sample; this is the 25% trimmed range, an example of an L-estimator. Other trimmed ranges, such as the interdecile range (10% trimmed range) can also be used. For a Gaussian distribution, IQR is related to as . Another familiar robust measure of scale is the median absolute deviation (MAD), the median of the absolute values of the differences between the data values and the overall median of the data set; for a Gaussian distribution, MAD is related to as (the derivation can be found here). Robust measures of scale can be used as estimators of properties of the population, either for parameter estimation or as estimators of their own expected value. For example, robust estimators of scale are used to estimate the population standard deviation, generally by multiplying by a scale factor to make it an unbiased consistent estimator; see scale parameter: estimation. For example, dividing the IQR by 2 erf−1(1/2) (approximately 1.

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.

Concepts associés (18)

Cours associés (17)

Séances de cours associées (134)

FIN-525: Financial big data

The course introduces modern methods to acquire, clean, and analyze large quantities of financial data efficiently. The second part expands on how to apply these techniques and robust statistics to fi

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

Indicateur de dispersion

En statistique, un indicateur de dispersion mesure la variabilité des valeurs d’une série statistique. Il est toujours positif et d’autant plus grand que les valeurs de la série sont étalées. Les plus courants sont la variance, l'écart-type et l'écart interquartile. Ces indicateurs complètent l’information apportée par les indicateurs de position ou de tendance centrale, mesurés par la moyenne ou la médiane. Dans la pratique, c'est-à-dire dans l'industrie, les laboratoires ou en métrologie, où s'effectuent des mesurages, cette dispersion est estimée par l'écart type.

Robust measures of scale

Interdecile range

In statistics, the interdecile range is the difference between the first and the ninth deciles (10% and 90%). The interdecile range is a measure of statistical dispersion of the values in a set of data, similar to the range and the interquartile range, and can be computed from the (non-parametric) seven-number summary. Despite its simplicity, the interdecile range of a sample drawn from a normal distribution can be divided by 2.56 to give a reasonably efficient estimator of the standard deviation of a normal distribution.

Régimes de traitement optimaux : approches variables instrumentales

Déplacez-vous dans des approches instrumentales variables pour des régimes de traitement optimaux, y compris la médecine de précision et des recommandations personnalisées, en mettant l'accent sur les conditions d'identification et les estimateurs robustes basés sur la classification.

Matlab: 3D Surface Plotting ME-213: Programmation pour ingénieur

Couvre les tableaux logiques, les tracés de surface 3D, les courbes paramétriques, l'interpolation et l'ajustement dans Matlab.

Bandits à bras multiples : Estimation de la distribution COM-406: Foundations of Data Science

Couvre les bandits multi-bras et l'estimation de la distribution, soulignant l'importance des estimateurs robustes.