6533b7dcfe1ef96bd1272b6f

RESEARCH PRODUCT

Quantile regression via iterative least squares computations

Mariangela SciandraLuigi AugugliaroVito M. R. Muggeo

subject

Statistics and ProbabilityMathematical optimizationEarly stoppingquantile regressionsmooth approximationApplied MathematicsRegression analysisLeast squaresQuantile regressionleast squareModeling and SimulationNon-linear least squaresApplied mathematicsStatistics Probability and UncertaintyTotal least squaresSettore SECS-S/01 - StatisticaQuantileParametric statisticsMathematics

description

We present an estimating framework for quantile regression where the usual L 1-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.

yearjournalcountryeditionlanguage
2012-11-01Journal of Statistical Computation and Simulation
https://doi.org/10.1080/00949655.2011.583650