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Variance stabilization for a scalar parameter
Author(s) -
DiCiccio Thomas J.,
Monti Anna Clara,
Alastair Young G.
Publication year - 2006
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2006.00544.x
Subject(s) - transformation (genetics) , parametric statistics , variance (accounting) , estimator , scalar (mathematics) , mathematics , nonparametric statistics , multivariate statistics , inference , range (aeronautics) , econometrics , statistics , computer science , artificial intelligence , geometry , accounting , biochemistry , chemistry , materials science , business , composite material , gene
Summary. We present a variance stabilizing transformation for inference about a scalar parameter that is estimated by a function of a multivariate M ‐estimator. The transformation proposed is automatic, computationally simple and can be applied quite generally. Though it is based on an intuitive notion and entirely empirical, the transformation is shown to have an appropriate justification in providing variance stabilization when viewed from both parametric and nonparametric perspectives. Further, the transformation repairs deficiencies of existing methods for variance stabilization. The transformation proposed is illustrated in a range of examples, and its effectiveness to yield confidence limits having low coverage error is demonstrated in a numerical example.