关于加权全最小一乘法.pdf

??????????????2009?4?Chinese Journal of Applied Probabilityand Statistics Apr. 2009?????????????????(ν??????????????,Ё?, 233030)??Ч???????Q(a, b, c) =1√a2+b2nPi=1wi|axi+byi+c|=min (wi>0, i= 1,2,· · ·, n)?,????ax+by+c= 0????,??????????????с???,???????????????????.???:????????,????,???,с???.?????: O171.§1.? ???n??Ч?:(x1, y1),(x2, y2),· · ·,(xn, yn),()?()?????????D.???????????????????,????????,????????(Robust)??,????????,????????????,????????[1].????????????????????????[2–5].?????????Q1(a, b) =nPi=1|yi?axi?b|= min()?,????a, b?????y=ax+b?;?????????????Q2(a, b) =1√1+a2nPi=1wi|yi?axi?b|= min (wi>0, i= 1,2,· · ·, n) ()?,????a, b?????y=ax+b?;Ч???????????:???Q(a, b, c) =1√a2+b2nPi=1wi|axi+byi+c|=min (wi>0, i= 1,2,· · ·, n) ()?ν???????????(2006KJ052C)??.Ч?2005?4?21???,2008?1?13??????.《应用概率统计》版权所有136????????????,????a,b, c?????ax+by+c= 0 (??(), ()????????y=ax+b??).?????,??????D???Ч????ax+by+c= 0??????????,?????????????????,?????????????.????????()??,????ax+by+c= 0????.§2.????????,?()?Q(a, b, c) = min?????????????????,??????????.?D??Ч????Dr:x2+y2=r2(r >0)?,???????,?с??Dr??,????????Dr????????????.?(x0, y0)∈Dr,?x20+y20=r2(r >0),??Dr??(x0, y0)???x0x+y0y=r2,??????????Dr??????:x0x+y0y=d(?r2≤d≤r2);?(x0, y0)??Dr????,??????Dr?????????????x0x+y0y?d= 0 (?r2≤d≤r2,(x0, y0)∈Dr).()D?????()?????????Q(x0, y0,?d) = (x20+y20)?1/2nPi=1wi|x0xi+