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The Method of Finite Difference Regression

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Document pages: 20 pages

Abstract: In this paper I present a novel polynomialregression method called Finite Difference Regression for a uniformly sampledsequence of noisy data points that determines the order of the best fittingpolynomial and provides estimates of its coefficients. Unlike classical least-squarespolynomial regression methods in the case where the order of the best fittingpolynomial is unknown and must be determined from the R2 value of the fit, I show how the t-test from statistics can be combined with the method of finite differencesto yield a more sensitive and objective measure of the order of the bestfitting polynomial. Furthermore, it is shown how these finite differences usedin the determination of the order, can be reemployed to produce excellentestimates of the coefficients of the best fitting polynomial. I show that notonly are these coefficients unbiased and consistent, but also that theasymptotic properties of the fit get better with increasing degrees of thefitting polynomial.

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