An Unbalanced Jackknife

It is proved that the jackknife estimate = n - (n - 1) (-₈/n) of a function = f () of the regression parameters in a general linear model Y = X + 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 -₈, which is the least squares estimate with the ith row deleted, and -₈ = f (-₈). The standard error of the pseudo-values ᵢ = n - (n - 1) -₈ is a consistent estimate of the asymptotic standard deviation of under similar conditions. Generalizations and applications are discussed.