Sharp asymptotics for isotonic regression
Sharp asymptotics for isotonic regression
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DOI：
10.1007/s004400100171
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发表时间：
2002-02
影响因子：
2
通讯作者：
C. Durot
中科院分区：
文献类型：
--
作者：
C. Durot
研究了单调回归函数的等渗估计量（即单调性限制下的最小二乘估计量）的渐近行为。特别地，证明了等渗估计器和真实函数之间的δ1-距离为n-1/3。此外，还证明了该 1-距离的中心版本以 then1/2 速率收敛到具有固定方差的高斯变量。
The asymptotic behavior of the isotonic estimator of a monotone regression function (that is the least-squares estimator under monotonicity restriction) is investigated. In particular it is proved that the ?1-distance between the isotonic estimator and the true function is of magnituden-1/3. Moreover, it is proved that a centered version of this ?1-distance converges at then1/2rate to a Gaussian variable with fixed variance.