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
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
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))
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.