Multivariate Least Median-of-Squares Estimator

Given a set P={p1,,pn}P = \{p_1, \dots, p_n\} of points in Rd\mathbb R^d, where pi=(xi,1,xi,2,,xi,d)p_i = (x_{i, 1}, x_{i, 2}, \dots, x_{i, d}), compute the parameter vector θ=(θ1,θ2,,θd)\theta = (\theta_1, \theta_2, \dots, \theta_d) that minimizes the median of the squared residuals (where a residual is defined as xi,d(xi,1θ1++xi,d1θd1+θd)x_{i, d}-(x_{i, 1}\theta_1 + \dots + x_{i, d-1}\theta_{d-1} + \theta_d)).

Parameters

  • nn: number of points in PP
  • dd: dimension of points

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Filters

Computational Model

Randomization

Approximation

Algorithms Table

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Reductions Table

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Other relevant algorithms

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