Penalized triograms: total variation regularization for bivariate smoothing

By Roger W. Koenker, Ivan Mizera. 2004

149 citations recorded by the source corpus.

Subfields: Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/935e41c8a9578de9c8b9104c442472f408f6b6e5

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In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Local linear spatial quantile regression (2009, methodology): “Very recently, Koenker and Mizera [30] made a first step towards a spatial quantile-based analysis by proposing, under the name of penalized triograms, a penalized spline method based on adaptively selected triangulations of the plane that allows for computing conditional quantiles over a two-dimens”
A fast and efficient implementation of qualitatively constrained quantile smoothing splines (2007, methodology): “…show that the factor of speed improvement between the sparse and dense versions of the Frisch-Newton algorithm ranges from roughly 36 at the sample size of 64 to approximately 850 at the sample size of 1024 when applied to a bivariate quantile smoothing via triogram of Koenker and Mizera (2004).”
Multiscale methods for data on graphs and irregular multidimensional situations (2009, methodology): “Hansen et al. (1998) introduced the triogram method for function estimation using piecewise linear bivariate splines based on an adaptively constructed triangulation (see also Koenker and Mizera (2004) for a smoothing spline approach to triograms based on the Delaunay triangulation).”
Asymmetric Loss Functions for Forecasting in Criminal Justice Settings (2011, methodology): “Very recently and based on work by Koenker and Mizera (2003) , the quantile regression procedures in R have been extended to include shrinkage options both for individual nonparametric functions of each regressor and for the overall regression fit.”
Nonparametric M-quantile regression using penalised splines (2009, unknown): “gif"/> – and nonparametric quantile regression 6 33 – <inline-graphic xmlns:xlink="http://www.”
Quantile Regression: Overview and Selected Applications ∗ (2004, background): “…(1) as: Fuτ (τ − x 0 iβτ |xi) = Pr(yi ≤ τ |xi) (6) which is essentially a different form derived from the more familiar: yi = x 0 iβτ + uτ i (7) noy (1994) or Koenker and Mizera (2003), and the references therein, for more information on these topics. where the distribution of the error term uτ…”
Inequality constrained quantile regression (2005, unknown): “See Koenker and Mizera (2002) for details.”
Accuracy assessment of digital elevation models by means of robust statistical methods (2009, methodology): “Using the Koenker and Mizera (2004) approach a continuous, piecewise linear function over an adaptively selected triangulation over the ( x , y ) plane for e.g. the 95% quantile of the absolute error distribution can thus be obtained.”
Linear quantile mixed models (2013, methodology): “Quantile smoothing of surfaces and related inference is a recent topic (He et al. 1998; He and Portnoy 2000; Koenker and Mizera 2004).”
Additive models for quantile regression: Model selection and confidence bandaids (2010, methodology): “The methods employ the total variation smoothing penalties introduced in Koenker, Ng and Portnoy (1994) for univariate components and Koenker and Mizera (2004) for bivariate components.”
Beyond mean regression (2013, unknown): “…the possible predictor structures is basically limited to additive model specifications (possibly comprising bivariate surfaces based on triograms; Koenker and Mizera, 2004), both the Bayesian formulation and boosting enable the application of the full potential of structured additive regression…”