Consistency of Smoothing with Running Linear Fits

Abstract

We establish the mean square consistency of running (ordinary) least squares linear regression smoothers, under realistic conditions on the joint distribution of the abscissa and ordinate (X and Y below) variables. The windows used in the running least squares fits need not be centered on the points for which they are used. In fact, we show that taking a window of points entirely to one side of a data point, fitting a line to that window and using the value of that line at the target point is consistent. It follows that the Supersmoother of Friedman and Stuetzle (1982) and the Split Linear Smoother of McDonald and Owen (1984) are both consistent. Keywords include: Smoothing; Nonparametric regression; Consistency.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1984
Accession Number
ADA150232

Entities

People

  • A. B. Owen
  • J. C. Marhoul

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Consistency

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Graph Algorithms and Convex Optimization.