Appendix C The Modern Way of Inference
C.1 Robust Estimation of Standard Errors In deriving the standard error of the least squares estimate or the maximum likelihood estimate in Appendix A.3 and Appendix B.3, the key argument was the fact that we could represent Δˆ j = βˆ j−β j as a linear combination
Δˆ j = a˜ j0h˜0 + a˜ j1h˜1 + a˜ j2h˜2 + . . .+ a˜ jph˜p (***) with some values a˜ jk (not depending on y1,y2, . . . , yn) and h˜0 = ∑ni=1 ei and h˜ j = ∑ni=1 xi jei for j = 1,2, . . . , p. We then were able to rewrite Δˆ j as a linear combination of the errors ei, and we could determine the variance of ei from our modelling assumptions.