TITLE:
The Method of Finite Difference Regression
AUTHORS:
Arjun Banerjee
KEYWORDS:
Polynomial Regression, t-Test, Finite Differences
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.1,
February
2,
2018
ABSTRACT: In this paper I present a novel polynomial
regression method called Finite Difference Regression for a uniformly sampled
sequence of noisy data points that determines the order of the best fitting
polynomial and provides estimates of its coefficients. Unlike classical least-squares
polynomial regression methods in the case where the order of the best fitting
polynomial 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 differences
to yield a more sensitive and objective measure of the order of the best
fitting polynomial. Furthermore, it is shown how these finite differences used
in the determination of the order, can be reemployed to produce excellent
estimates of the coefficients of the best fitting polynomial. I show that not
only are these coefficients unbiased and consistent, but also that the
asymptotic properties of the fit get better with increasing degrees of the
fitting polynomial.