An O(n) algorithm for weighted least squares regression by integer quasi-convex and unimodal or umbrella functions

doi:10.1016/j.camwa.2009.04.003

Computers & Mathematics with Applications

Volume 58, Issue 4, August 2009, Pages 776-783

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Abstract

The problem of fitting $n$ data points by an integer quasi-convex (also quasi-concave, umbrella or unimodal) function using the weighted least squares distance function is considered. An algorithm of linear time ( $O (n)$ ) worst-case complexity and thus optimal is constructed for computing a best fit. This problem arises in the context of curve fitting or statistical estimation.

Keywords

Least squares regression

Integer quasi-convex regression

Integer unimodal regression

Integer umbrella regression

Umbrella ordering

Isotonic regression

Linear time algorithms

Greatest convex minorant (GCM)

Least concave majorant (LCM)