Quantile regression via iterative least squares computations

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Abstract

We present an estimating framework for quantile regression where the usual L1-norm objective function is replaced by its smooth parametric approximation. An exact path-following algorithm is derived, leading to the well-known ‘basic’ solutions interpolating exactly a number of observations equal to the number of parameters being estimated. We discuss briefly possible practical implications of the proposed approach, such as early stopping for large data sets, confidence intervals, and additional topics for future research.
Lingua originaleEnglish
pagine (da-a)1557-1569
Numero di pagine0
RivistaJournal of Statistical Computation and Simulation
Volume82
Stato di pubblicazionePublished - 2012

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Quantile Regression
Least Squares
Early Stopping
Path-following Algorithm
L1-norm
Exact Algorithms
Large Data Sets
Confidence interval
Objective function
Approximation
Least squares
Quantile regression
Framework
Observation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics
  • Statistics, Probability and Uncertainty
  • Modelling and Simulation

Cita questo

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abstract = "We present an estimating framework for quantile regression where the usual L1-norm objective function is replaced by its smooth parametric approximation. An exact path-following algorithm is derived, leading to the well-known ‘basic’ solutions interpolating exactly a number of observations equal to the number of parameters being estimated. We discuss briefly possible practical implications of the proposed approach, such as early stopping for large data sets, confidence intervals, and additional topics for future research.",
keywords = "quantile regression; least squares; smooth approximation",
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AU - Sciandra, Mariangela

AU - Augugliaro, Luigi

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AB - We present an estimating framework for quantile regression where the usual L1-norm objective function is replaced by its smooth parametric approximation. An exact path-following algorithm is derived, leading to the well-known ‘basic’ solutions interpolating exactly a number of observations equal to the number of parameters being estimated. We discuss briefly possible practical implications of the proposed approach, such as early stopping for large data sets, confidence intervals, and additional topics for future research.

KW - quantile regression; least squares; smooth approximation

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