S-estimator (original) (raw)
The goal of S-estimators is to have a simple high-breakdown regression estimator, which share the flexibility and nice asymptotic properties of M-estimators. The name "S-estimators" was chosen as they are based on estimators of scale. We will consider estimators of scale defined by a function , which satisfy * R1 – is symmetric, continuously differentiable and . * R2 – there exists such that is strictly increasing on For any sample of real numbers, we define the scale estimate as the solution of , Definition: and the final scale estimator is then .
| Property | Value |
|---|---|
| dbo:abstract | The goal of S-estimators is to have a simple high-breakdown regression estimator, which share the flexibility and nice asymptotic properties of M-estimators. The name "S-estimators" was chosen as they are based on estimators of scale. We will consider estimators of scale defined by a function , which satisfy * R1 – is symmetric, continuously differentiable and . * R2 – there exists such that is strictly increasing on For any sample of real numbers, we define the scale estimate as the solution of , where is the expectation value of for a standard normal distribution. (If there are more solutions to the above equation, then we take the one with the smallest solution for s; if there is no solution, then we put .) Definition: Let be a sample of regression data with p-dimensional . For each vector , we obtain residuals by solving the equation of scale above, where satisfy R1 and R2. The S-estimator is defined by and the final scale estimator is then . (en) |
| dbo:wikiPageID | 49892110 (xsd:integer) |
| dbo:wikiPageLength | 2024 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1028707051 (xsd:integer) |
| dbo:wikiPageWikiLink | dbc:Robust_regression dbc:Estimator dbr:Linear_regression dbr:Expected_value dbr:Normal_distribution dbr:Differentiable_function dbr:Robust_statistics dbr:M-estimators |
| dcterms:subject | dbc:Robust_regression dbc:Estimator |
| rdfs:comment | The goal of S-estimators is to have a simple high-breakdown regression estimator, which share the flexibility and nice asymptotic properties of M-estimators. The name "S-estimators" was chosen as they are based on estimators of scale. We will consider estimators of scale defined by a function , which satisfy * R1 – is symmetric, continuously differentiable and . * R2 – there exists such that is strictly increasing on For any sample of real numbers, we define the scale estimate as the solution of , Definition: and the final scale estimator is then . (en) |
| rdfs:label | S-estimator (en) |
| owl:sameAs | wikidata:S-estimator https://global.dbpedia.org/id/2PMjG |
| prov:wasDerivedFrom | wikipedia-en:S-estimator?oldid=1028707051&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:S-estimator |
| is dbo:wikiPageWikiLink of | dbr:M-estimator dbr:Peter_Rousseeuw |
| is foaf:primaryTopic of | wikipedia-en:S-estimator |