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A Note on the Estimation of Non‐Differentiable Functions of MuItinomial ProbabiIities
Author(s) -
Weba M.
Publication year - 1992
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1992.tb01342.x
Subject(s) - differentiable function , mathematics , estimator , multinomial distribution , mean squared error , function (biology) , statistics , mathematical analysis , biology , evolutionary biology
. Consider the problem of estimating f(θ ) where fis a given function and 8 is the unknown parameter of a multinomial distribution. In order to describe the asymptotic behaviour of the frequency substitution estimator, conventional methods typically require differentiability of f , and the error representations depend on the unknown parameter θ. In this note, a pararneter‐free bound for the mean square error is derived which requires continuity of f only.