The Fisher-Neyman Factorization Theorem gives a criterion for a statistic to be sufficient for a parameter, stating that a statistic is sufficient if and only if the likelihood function can be factored into a piece depending on the data only through that statistic and a separate piece not depending on the parameter. Named for Ronald Fisher and Jerzy Neyman, it is the standard tool used to identify sufficient statistics in parametric statistical models.
Facts
Classification
Statement Form Statement FormCharacterization Theorem 1 StatementA statistic T is sufficient for the parameter theta if and only if the density can be factored as f(x;theta) = h(x) g(theta, T(x)) for nonnegative functions g and h. 1 Connections
Has Statement Form
In Branch
Proved By
Source Sufficient statistic (Wikipedia)
Sources
1. Fisher-Neyman factorization theorem (Wikipedia)
Statement sectionQuote, Statement section
If the probability density function is ƒ(x;θ), where θ is a parameter, then T is sufficient for θ if and only if nonnegative functions g and h can be found such that f(x;θ)=h(x)g(θ,T(x))
Sufficient statistic (Wikipedia)
Proved By: Ronald Fisher, Lead paragraphQuote, Proved By: Ronald Fisher, Lead paragraph
The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in descriptive statistics
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.