Quantile Regression via an MM Algorithm

By David R. Hunter, Kenneth L. Lange. 2000

368 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/68e773952ae478424af99f9aaa90e2737a452d81

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

A new method to analyse relationships between yield components with boundary lines (2007, methodology): “When the function is nonlinear, equation (8) can be minimised by using an interior point algorithm (Koenker and Park, 1996) or the MM algorithm developed by Hunter and Lange (2000). The former is implemented in the function nlrq of the package quantreg that can be freely downloaded from CRAN: http:/”
Generative adversarial network-based approach to signal reconstruction from magnitude spectrogram (2018, background): “According to the principle of the majorization-minimization algorithm [9], it can be shown that J (φ, c̃) ≡ ∥a ⊙ φ− c̃∥(2)2 is a majorizer of J (φ) where c̃ ∈ C is an auxiliary variable and a stationary point of J (φ) can be found by iteratively performing the following updates:”
A Finite Smoothing Algorithm for Quantile Regression (2007, methodology): “The interior point algorithm was introduced into quantile regression by Koenker and Park (1996) with an emphasis on nonlinear quantile regression. This version of interior point algorithm follows the affine scaling algorithm of Vanderbei, Meketon, and Freedman (1986). A better implementation of the ”
A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems (2013, methodology): “We can easily show that Thus, the GIST algorithm is equivalent to solving a sequence of minimization problems: and can be interpreted as the well-known Majorization and Minimization (MM) technique (Hunter & Lange, 2000).”
An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression (2015, methodology): “For unpenalized quantile regression, Koenker and Park (1996) proposed a useful interior point algorithm, and Hunter and Lange (2000) developed an effective MM algorithm which majorizes the quantile loss function by a quadratic function.”
A Tutorial on MM Algorithms (2004, background): “One can readily prove (Hunter and Lange 2000b) that for q 2 (0 ; 1) , a q th sample quantile of x 1 ; : : : ; x n minimizes the function where » q ( ‡ ) is the “vee” function When q = 1 = 2 , this function is proportional to the absolute value function; for q 6 = 1 = 2 , the “vee” is tilted to one…”
Efficient Quantile Regression Analysis With Missing Observations (2015, methodology): “Following Hunter and Lange (2000), we consider the quadratic function ζ ετ ( | k) = 1 4 [ 2 ε + | k| + (4τ − 2) + c ] as the surrogate function for ρετ ( ), where ρ ε τ ( ) = ρτ ( ) − ε 2 log(ε + |”
Conformalized Quantile Regression (2019, methodology): “Even for highly heteroscedastic data, this methodology has been shown to be adaptive to local variability [19–25].”
Optimization Transfer Using Surrogate Objective Functions (2000, methodology): “Among these algorithms are methods for convex programming (Lange, 1994), multinomial logistic regression (B¨ohning, 1992), quantile regression (Hunter and Lange, 2000), and estimation in proportional hazards and proportional odds models (B¨ohning and Lindsay, 1988; Hunter and Lange, 2000).”