1. For any s ? N , this directly follows from ? s (cy it ) = c? s y it , ? s (y it + x it v) = ? s y it + (? s x it ) v, and ? s (x it A) = (? s x it ) A. Proof of Theorem 1: Before applying the LTS estimator;APPENDIX: PROOFS Proof of Lemma 1: Since the LTS estimator is regression, affine, and scale equivariant (Rousseeuw and Leroy,1987
2. In the case of the first differences, this means that LTS breaks down if min{2, T ? 1}m > nT (T) ? h nT , implying that the breakdown point of the proposed panel-data LTS estimator equals (nT (T) ? h nT );LTS thus breaks down only if the number of outliers exceeds nT (T) ? h nT
3. Commentary