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| A Necessary and Sufficient Condition for Convergence of Error Probability Estimates in K-NN Discrimination |
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Citation： |
Sun Zhigang.A Necessary and Sufficient Condition for Convergence of Error Probability Estimates in K-NN Discrimination[J].Chinese Annals of Mathematics B,1985,6(4):439~444 |
| Page view： 845
Net amount： 862 |
Authors： |
Sun Zhigang; |
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| Abstract： |
Let(X, \theta)be R^d \times{1,\cdots, s} valued random vector,(X_j,\theta_j), j=1,\cdots, n, be its observed values,\theta_nj be the K-nearest neighbor estimate of \theta_j, R^(k) be the limit of error probability and be $[\hat R]_nk\triangleq 1/n[\sum\limits_{j = 1}^n {{I_{({\theta _j} \ne \theta _{nj}^{(k)})}}} \]$ be the error probability estimate. In this paper it is shown that \forall \varepsilon>0, \exists constants a>0, c<\infinity such that
$P(|[\hat R]_nk-R^(k)|>\varepsilon) |
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