Strong consistency of automatic kernel regression estimates
Strong consistency of automatic kernel regression estimates
复制标题
自动核回归估计的强一致性
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Harro Walk
中科院分区：
文献类型：
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作者：
M. Kohler;A. Krzyżak;Harro Walk
考虑来自独立且同分布的有界数据的回归函数估计。相对于设计测量的积分的L2误差被用作误差标准。结果表明，只要从某个确定性区间中选择随机带宽，且其上限和下限满足用于证明确定性带宽核估计一致性的通常条件，则具有任意随机带宽的核回归估计对于所有分布都是弱一致和强一致的。通过交叉验证选择离散带宽可以削弱带宽条件。
Regression function estimation from independent and identically distributed bounded data is considered. TheL2 error with integration with respect to the design measure is used as an error criterion. It is shown that the kernel regression estimate with an arbitrary random bandwidth is weakly and strongly consistent forall distributions whenever the random bandwidth is chosen from some deterministic interval whose upper and lower bounds satisfy the usual conditions used to prove consistency of the kernel estimate for deterministic bandwidths. Choosing discrete bandwidths by cross-validation allows to weaken the conditions on the bandwidths.