异方差回归模型近邻型估计的相合性

本文研究异方差回归模型Ｙｉ＾（ｎ）＝ｇ（ｘｉ＾（ｎ））＋εｉ＾（ｎ）,ｉ＝１,…,ｎ,其中ｇ是右实函数,ｘｉ＾（ｎ）是非随机设计点列,εｉ＾（ｎ）是随机误差,文中定义了一类ｇ（ｘ）的近邻型估计ｇｎ（ｘ）＝（ｎ）∑（ｉ＝１）Ｗｍ（ｘ）Ｙｉ＾（ｎ）,得到了ｒ阶平均相全和渐近正态性,特别,在（∞）∑（ｎ＝１）（ｎ）∑（ｉ＝１）Ｅ／εｉ＾（ｎ）／＾ｓ／（ｎｉ）＾ｓ／ｒ〈∞,ｍａｘＥ（１≤ｉ≤ｎ）／εｉ（＾     

FIXED-DESIGN REGRESSION FOR LINEARTIME SERIES

1 IntroductionLet A be a subset of tlie real line R. Consider a fixed design regression modelYni = g(Z.i) + Eni, 0 S i S n, (1.1)liere xnot', xnn E A, are design points, En1,' f Enn are randon errors f g is an unknownfnnctiou. Assunle that for each nl {E.i, 0 5 i S n} have the saxne distribution as {(i, 0 5 i S n},where (f is a general weakly stationary llnear processhere {Z,} is a nurtingale dtherence sequence ralative to an increasing sequence of J-fields Rcosuch that E(ZllR--,) …