Cumulant Coefficients for Studentized Estimates

Let ŵ estimate w ∈ RP, the parameters in a parametric model. Starting with its asymptotic covariance, bias and skewness, the leading cumulant coefficients of ŵ are the building blocks for analytic statistical inference on w. Similarly, for any function t(w), the leading cumulant coefficients of its Studentized form are needed for analytic statistical inference on t(w). We give these cumulant coefficients in terms of those of ŵ and the derivatives of t(w) at w.