Degree of Local Polynomials
The local polynomials fit to each subset of the data are almost always of first or second degree; that is, either locally linear (in the straight line sense) or locally quadratic. Using a zero degree polynomial turns LOESS into a weighted moving average. Such a simple local model might work well for some situations, but may not always approximate the underlying function well enough. Higher-degree polynomials would work in theory, but yield models that are not really in the spirit of LOESS. LOESS is based on the ideas that any function can be well approximated in a small neighborhood by a low-order polynomial and that simple models can be fit to data easily. High-degree polynomials would tend to overfit the data in each subset and are numerically unstable, making accurate computations difficult.
Read more about this topic: Local Regression
Famous quotes containing the words degree of, degree and/or local:
“[F]or as Socrates says that a wise man is a citizen of the world, so I thought that a wise woman was equally at liberty to range through every station or degree of men, to fix her choice wherever she pleased.”
—Sarah Fielding (1710–1768)
“Nothing in life possesses value except the degree of power—assuming that life itself is the will to power.”
—Friedrich Nietzsche (1844–1900)
“The local is a shabby thing. There’s nothing worse than bringing us back down to our own little corner, our own territory, the radiant promiscuity of the face to face. A culture which has taken the risk of the universal, must perish by the universal.”
—Jean Baudrillard (b. 1929)