Report on Local Linear Regression

[Dirk Ormoneit]

The following technical report is now available on-line at

http://www-stat.stanford.edu/~ormoneit/tr-1999-11.ps

Best,

Dirk

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        OPTIMAL KERNEL SHAPES FOR LOCAL LINEAR REGRESSION
                        by
          Dirk Ormoneit and Trevor Hastie

Local linear regression performs very well in many low-dimensional forecasting
problems. In high-dimensional spaces, its performance typically decays due to
the well-known ``curse-of-dimensionality''.  Specifically, the volume of a
weighting kernel that contains a fixed number of samples increases exponentially
with the number of dimensions. The bias of a local linear estimate may thus
become unacceptable for many real-world data sets. A possible way to control
the bias is by varying the ``shape'' of the weighting kernel. In this work we
suggest a new, data-driven method to estimating the optimal kernel shape.
Experiments using two artificially generated data sets and data from the UC
Irvine repository show the benefits of kernel shaping.


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Dirk Ormoneit
Department of Statistics, Room 206
Stanford University
Stanford, CA 94305-4065

ph.: (650) 725-6148
fax: (650) 725-8977

ormoneit at stat.stanford.edu
http://www-stat.stanford.edu/~ormoneit/