Abstract
Let X 1, X 2,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with X i we observe Y i drawn from an unknown conditional distribution F(y|X i = x) with continuous regression function m(x) = E[Y|X = x]. The problem of interest is to estimate Y n based on X n and the data {(X i, Y i)} i=1 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 1, X 2, ....
Original language | English (US) |
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Pages (from-to) | 2785-2788 |
Number of pages | 4 |
Journal | IEEE Transactions on Information Theory |
Volume | 48 |
Issue number | 10 |
DOIs | |
State | Published - Oct 2002 |
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences
Keywords
- Arbitrary random processes
- Consistency
- Data dependent
- Kernel estimate
- Nearest neighbor estimate
- Nonparametric regression