Estimating the Bias of Local Polynomial Approximation Methods Using the Peano Kernel
The determination of uncertainty of an estimate requires both the variance and the bias of the estimate. Calculating the variance of local polynomial approximation (LPA) estimates is straightforward. We present a method, using the Peano Kernel Theorem, to estimate the bias of LPA estimates and show how this can be used to optimize the LPA parameters in terms of the bias-variance tradeoff. Figures of merit are derived and values calculated for several common methods. The results in the literature are expanded by giving bias error bounds that are valid for all lengths of the smoothing interval, generalizing the currently available asymptotic results that are only valid in the limit as the length of this interval goes to zero.
- Research Organization:
- Nevada Test Site (NTS), Mercury, NV (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
- DOE Contract Number:
- AC52-06NA25946
- OSTI ID:
- 1136515
- Report Number(s):
- DOE/NV/25946-1551
- Journal Information:
- Contemporary Mathematics, Vol. 586; Conference: Eighth International Conference on Scientific Computing and Applications, University of Nevada, Las Vegas, Nevada, April 1-4, 2012; ISSN 0271-4132
- Country of Publication:
- United States
- Language:
- English
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