Journal of the Korean Statistical Society
- 제21권2호
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- Pages.153-166
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- 1992
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- 1226-3192(pISSN)
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- 2005-2863(eISSN)
Optimal Rates of Convergence in Tensor Sobolev Space Regression
초록
Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.