caa a22 4500 386385025 CHVBK 20180307112055.0 cr unu---uuuuu 161130e198909 xx s 000 0 eng 10.1017/S0305004100078166 doi S0305004100078166 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100078166 Influence of design on the rate of convergence to normality in L1 regression [Elektronische Daten] We provide a concise account of the influence of design variables on the convergence rate in an L1 regression problem. In particular, we show that the convergence rate may be characterized precisely in terms of third and fourth moments of the design variables. This result leads to necessary and sufficient conditions on the design for the Berry-Esseen rate to be achieved. We also show that a moment condition on the error distribution is necessary and sufficient for a non-uniform Berry-Esseen theorem, and that an Edgeworth expansion is possible if the design points are not too clumped. Copyright © Cambridge Philosophical Society 1989 Hall Peter Statistics Department, Australian National University, Canberra, Australia Welsh A. H. Statistics Department, Australian National University, Canberra, Australia Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/2(1989-09), 355-368 0305-0041 106:2<355 1989 106 PSP https://doi.org/10.1017/S0305004100078166 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100078166 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hall Peter Statistics Department, Australian National University, Canberra, Australia NATIONALLICENCE 700 1- Welsh A. H. Statistics Department, Australian National University, Canberra, Australia NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/2(1989-09), 355-368 0305-0041 106:2<355 1989 106 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge