Data-dependent k/sub n/-NN and kernel estimators consistent for arbitrary processes

Kulkarni S.R.; Posner S.E.; Sandilya S.

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Data-dependent k/sub n/-NN and kernel estimators consistent for arbitrary processes

机译：数据相关的k / sub n / -NN和核估计量对任意过程均一致

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Let X/sub 1/, X/sub 2/,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with X/sub i/ we observe Y/sub i/ drawn from an unknown conditional distribution F(y|X/sub i/=x) with continuous regression function m(x)=E[Y|X=x]. The problem of interest is to estimate Y/sub n/ based on X/sub n/ and the data {(X/sub i/, Y/sub i/)}/sub i=1//sup n-1/. We construct appropriate data-dependent nearest neighbor and kernel estimators and show, with a very elementary proof, that these are consistent for every process X/sub 1/, X/sub 2/,.

机译：令X / sub 1 /，X / sub 2 /，...是一个任意随机过程，它在可分离度量空间的完全有界子集中取值。与X / sub i /关联，我们观察到Y / sub i /是从未知条件分布F（y | X / sub i / = x）中提取的，具有连续回归函数m（x）= E [Y | X = x]。感兴趣的问题是基于X / sub n /和数据{（X / sub i /，Y / sub i /）} / sub i = 1 // sup n-1 /来估计Y / sub n /。我们构造了适当的数据相关的最近邻估计和核估计，并用非常基本的证据证明了对于每个过程X / sub 1 /，X / sub 2 /，它们都是一致的。

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来源
《IEEE Transactions on Information Theory》 |2002年第10期|p.2785-2788|共4页
作者
Kulkarni S.R.; Posner S.E.; Sandilya S.;
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作者单位

Dept. of Electr. Eng., Princeton Univ., NJ, USA;

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原文格式 PDF
正文语种 eng
中图分类无线电电子学、电信技术;
关键词
random processes; parameter estimation; set theory; kernel estimators; arbitrary random process; totally bounded subset; separable metric space; conditional distribution; continuous regression function; data-dependent nearest neighbor estimator;

机译：随机过程;参数估计;集合论核估计器;任意随机过程;完全有界子集;可分离的度量空间;有条件分配连续回归函数数据相关的最近邻居估计量;

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Data-dependent k/sub n/-NN and kernel estimators consistent for arbitrary processes

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