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Title: Error Estimates Derived from the Data for Least-Squares Spline Fitting

Publication Date:
Research Org.:
National Security Technologies, LLC
Sponsoring Org.:
USDOE - National Nuclear Security Administration (NNSA)
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Resource Relation:
Conference: 2007 IEEE Instrumentation and Measurement Technology Conference; Warsaw, Poland; May 2007
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Data smoothing, multi-resolution analysis, spline functions, estimation

Citation Formats

Jerome Blair. Error Estimates Derived from the Data for Least-Squares Spline Fitting. United States: N. p., 2007. Web.
Jerome Blair. Error Estimates Derived from the Data for Least-Squares Spline Fitting. United States.
Jerome Blair. Tue . "Error Estimates Derived from the Data for Least-Squares Spline Fitting". United States. doi:.
title = {Error Estimates Derived from the Data for Least-Squares Spline Fitting},
author = {Jerome Blair},
abstractNote = {},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}

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  • The use of least-squares fitting by cubic splines for the purpose of noise reduction in measured data is studied. Splines with variable mesh size are considered. The error, the difference between the input signal and its estimate, is divided into two sources: the R-error, which depends only on the noise and increases with decreasing mesh size, and the Ferror, which depends only on the signal and decreases with decreasing mesh size. The estimation of both errors as a function of time is demonstrated. The R-error estimation requires knowledge of the statistics of the noise and uses well-known methods. The primarymore » contribution of the paper is a method for estimating the F-error that requires no prior knowledge of the signal except that it has four derivatives. It is calculated from the difference between two different spline fits to the data and is illustrated with Monte Carlo simulations and with an example.« less
  • An automatic data-smoothing algorithm for data from digital oscilloscopes is described. The algorithm adjusts the bandwidth of the filtering as a function of time to provide minimum mean squared error at each time. It produces an estimate of the root-mean-square error as a function of time and does so without any statistical assumptions about the unknown signal. The algorithm is based on least-squares fitting to the data of cubic spline functions.
  • The method employed to curve-fit the exponential and Bessel functions as described can be adapted readily to curve-fit any function that can be expanded in a power series or is itself a polynomial of any order. The reason why these two functions were singled out is that they are the ones most frequently encountered in nuclear reactor laboratory experimentation: the exponential function with half-life and radiation beam attenuation and the Bessel function in the radial neutron flux distribution in homogeneous circular cylindrical geometry. The method has proved itself to be exceedingly useful and is remarkably easy to implement and execute.