Univariate Least-Quantile Squares Estimator

Given a set P={p1,,pn}P = \{p_1, \dots, p_n\} of points in R2\mathbb R^2, where pi=(xi,yi)p_i = (x_i, y_i), and a parameter 3kn3\leq k\leq n, compute the parameter vector θ=(θ1,θ2)\theta = (\theta_1, \theta_2) that minimizes the kkth smallest squared residual (where a residual is defined as yixiθ1θ2y_i - x_i\theta_1 - \theta_2).

Parameters

  • nn: number of points in PP
  • kk: quantile parameter

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Computational Model

Randomization

Approximation

Algorithms Table

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Reductions Table

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Other relevant algorithms

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