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\sum_{i=1}^n w_i(x) \left | Y_i - \beta_0 - \ldots - \beta_p(x_i-x)^p \right |
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results; this does not require a scale parameter. When <math>p=0</math>, this criterion is minimized by a locally weighted median; local <math>L_1</math> regression can be interpreted as 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 (mathematician)|M.C. Jones]] (1998).<ref>{{citation |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==
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