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Estimation by Maximum Entropy Subject to Second‐Order Conditions
Author(s) -
Lefkovitch L. P.
Publication year - 1989
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710310110
Subject(s) - mathematics , principle of maximum entropy , maximum entropy probability distribution , maximum entropy spectral estimation , statistics , entropy (arrow of time) , variance (accounting) , binary entropy function , physics , business , accounting , quantum mechanics
Abstract If the variance, V = V (μ, ϑ) is some known function of the mean, μ = μ(β), where ϑ and β may include unknown parameters, then given empirical data, this paper describes how to estimate the unknown parameters by choosing them to satisfy the variance/mean relationship, and simultaneously to require that the sampling probability distribution has maximum entropy. Bounds for the estimated values of the unknown parameters can be obtained by a further application of the maximum entropy principle. The power variance function, V (μ)=λμ ϑ is discussed, including some special cases of λ and ϑ. The procedure is briefly compared with quasi‐ likelihood, and illustrated by some numerical examples.