Variance stabilization for a scalar parameter

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. Copyright 2006 Royal Statistical Society.