Optimal Rates of Convergence for Tensor Spline Regression Estimators

  • Koo, Ja-Yong (Department of Statistics, Hallym University, Chunchon)
  • 발행 : 1990.12.01

초록

Let (X, Y) be a pair random variables and let f denote the regression function of the response Y on the measurement variable X. Let K(f) denote a derivative of f. The least squares method is used to obtain a tensor spline estimator $\hat{f}$ of f based on a random sample of size n from the distribution of (X, Y). Under some mild conditions, it is shown that $K(\hat{f})$ achieves the optimal rate of convergence for the estimation of K(f) in $L_2$ and $L_{\infty}$ norms.

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