Fisher consistency

Fisher consistency is a description of a statistical construct, used to describe probable outcomes within a certain set of "consistent outcomes". [ cite journal|title=Fisher Consistency of AM-Estimates of the Autoregression Parameter Using Hard Rejection Filter Cleaners|journal= Defense Technical Information Center OAI-PMH Repository (United States)|date=1988|first=R.D.|last=Martin|coauthors=Yohai, Victor , WASHINGTON UNIV SEATTLE DEPT OF STATISTICS |volume=|issue=|pages=|id= |url=|format=|accessdate=2008-09-15 ] It most often used to decide if an economic calculation is useful for modeling by determining the likelihood it will match along the lines of interest, in terms of probability curves, but it can be applied in various fields of science, most often chemistry and astrophysics. An estimate that is Fisher-consistent is more likely to produce useful information when applied to other related data sets.

Formula

Where "E" is the estimate and "L" is a proper likelihood function, "L" gives an estimate for "b" which meets the requirements for being Fisher-consistent if

: $Eleft\; [\; frac\{dln\; L\}\{db\}\; ight]\; =\; 0\; ext\{\; at\; \}b=b\_0,\; ,$

where "b"₀ represents "b"'s most basic value. [cite book | last = Jurečková | first = Jana | authorlink = | coauthors = Jan Picek | title = Robust Statistical Methods with R | publisher = CRC Press | date = 2006 | location = | pages = | url = | doi = | id = | isbn = 1584884541 ]

References