This preview shows pages 83–88. Sign up to view the full content.
−1∑i1nXin−2∑i1nVarXin−2∑i1n/n.As in the univariate case,VarX̄nconverges to zero at rate 1/n.83
has intentionally blurred sections.
Sign up to view the full version.
∙The multivariate CLT implies thatVarX̄n−1/2X̄n−−1/2nX̄n−d→Normal0,Ik∙Note that the standardized random vectorZn≡−1/2nX̄n−hasEZn0andVarZnIk.∙We can instead writenX̄n−d→Normal0,84