Local regression: Difference between revisions

Revision as of 09:03, 15 February 2025

Revision as of 02:35, 16 February 2025

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and a robust global estimate of the scale parameter.

If <math>\rho(u)=|u|</math>, the local <math>L_1</math> criterion

criterion

<math display="block">

\sum_{i=1}^n w_i(x) \left | Y_i - \beta_0 - \ldots - \beta_p(x_i-x)^p \right |

</math>

results; this does not require a scale parameter. LocalWhen <math>p=0</math>, this criterion is minimized by a locally-weighted median; local <math>L_1</math> regression hascan beenbe studiedinterpreted byas estimating the ''median'', rather than ''mean'', response. If the loss function is skewed, this becomes local quantile regression. See [[Keming Yu]] and [[M.C. Jones]] (1998),.<ref>{{cite |first1=Keming|last1=Yu|first2=M.C.|last2=Jones|title=Local Linear Quantile Regression|journal=Journal of the American Statistical Association|volume=93|pages=228-237}}</ref>

==Advantages==