An Unbalanced Jackknife

Abstract

It is proved that the jackknife estimate θ = nθ - (n - 1)( θ-i/n) of a function θ = f(β) of the regression parameters in a general linear model Y = Xβ + e is asymptotically normally distributed under conditions that do not require e to be normally distributed. The jackknife is applied by deleting in succession each row of the X matrix and Y vector in order to compute hatmathbfbeta-i , which is the least squares estimate with the ith row deleted, and θ-i = f(β-i). The standard error of the pseudo-values θi = nθ - (n - 1)θ-i is a consistent estimate of the asymptotic standard deviation of θ under similar conditions. Generalizations and applications are discussed.