Open Access
March 1998 Optimal design for curve estimation by local linear smoothing
Ming-Yen Cheng, Peter Hall, D. Michael Titterington
Bernoulli 4(1): 3-14 (March 1998).


The integral of the mean squared error of an estimator of a regression function is used as a criterion for defining an optimal design measure in the context of local linear regression, when the bandwidth is chosen in a locally optimal manner. An algorithm is proposed that constructs a sequence of piecewise uniform designs with the help of current estimates of the integral of the mean squared error. These estimates do not require direct estimation of the second derivative of the regression function. Asymptotic properties of the algorithm are established and numerical results illustrate the gains that can be made, relative to a uniform design, by using the optimal design or sub-optimal, piecewise uniform designs. The behaviour of the algorithm in practice is also illustrated.


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Ming-Yen Cheng. Peter Hall. D. Michael Titterington. "Optimal design for curve estimation by local linear smoothing." Bernoulli 4 (1) 3 - 14, March 1998.


Published: March 1998
First available in Project Euclid: 6 April 2007

zbMATH: 0894.62085
MathSciNet: MR1611863

Keywords: Bandwidth choice , local linear regression , mean squared error , Nonlinear regression , optimal design , sequential design

Rights: Copyright © 1998 Bernoulli Society for Mathematical Statistics and Probability

Vol.4 • No. 1 • March 1998
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