Degrees of freedom for piecewise Lipschitz estimators

Research output: Contribution to journalJournal articlepeer-review

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Degrees of freedom for piecewise Lipschitz estimators. / Mikkelsen, Frederik Riis; Hansen, Niels Richard.

In: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 54, No. 2, 01.05.2018, p. 819-841.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Mikkelsen, FR & Hansen, NR 2018, 'Degrees of freedom for piecewise Lipschitz estimators', Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol. 54, no. 2, pp. 819-841. https://doi.org/10.1214/17-AIHP822

APA

Mikkelsen, F. R., & Hansen, N. R. (2018). Degrees of freedom for piecewise Lipschitz estimators. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 54(2), 819-841. https://doi.org/10.1214/17-AIHP822

Vancouver

Mikkelsen FR, Hansen NR. Degrees of freedom for piecewise Lipschitz estimators. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. 2018 May 1;54(2):819-841. https://doi.org/10.1214/17-AIHP822

Author

Mikkelsen, Frederik Riis ; Hansen, Niels Richard. / Degrees of freedom for piecewise Lipschitz estimators. In: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. 2018 ; Vol. 54, No. 2. pp. 819-841.

Bibtex

@article{60609f59635646babc4a4f193d2f4d1b,
title = "Degrees of freedom for piecewise Lipschitz estimators",
abstract = "A representation of the degrees of freedom akin to Stein{\textquoteright}s lemma is given for a class of estimators of a mean valueparameter in Rn. Contrary to previous results our representation holds for a range of discontinues estimators. It shows that eventhough the discontinuities form a Lebesgue null set, they cannot be ignored when computing degrees of freedom. Estimatorswith discontinuities arise naturally in regression if data driven variable selection is used. Two such examples, namely best subsetselection and lasso-OLS, are considered in detail in this paper. For lasso-OLS the general representation leads to an estimateof the degrees of freedom based on the lasso solution path, which in turn can be used for estimating the risk of lasso-OLS.A similar estimate is proposed for best subset selection. The usefulness of the risk estimates for selecting the number of variablesis demonstrated via simulations with a particular focus on lasso-OLS.",
author = "Mikkelsen, {Frederik Riis} and Hansen, {Niels Richard}",
year = "2018",
month = may,
day = "1",
doi = "10.1214/17-AIHP822",
language = "English",
volume = "54",
pages = "819--841",
journal = "Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques",
issn = "0246-0203",
publisher = "Institute Henri Poincar{\'e}",
number = "2",

}

RIS

TY - JOUR

T1 - Degrees of freedom for piecewise Lipschitz estimators

AU - Mikkelsen, Frederik Riis

AU - Hansen, Niels Richard

PY - 2018/5/1

Y1 - 2018/5/1

N2 - A representation of the degrees of freedom akin to Stein’s lemma is given for a class of estimators of a mean valueparameter in Rn. Contrary to previous results our representation holds for a range of discontinues estimators. It shows that eventhough the discontinuities form a Lebesgue null set, they cannot be ignored when computing degrees of freedom. Estimatorswith discontinuities arise naturally in regression if data driven variable selection is used. Two such examples, namely best subsetselection and lasso-OLS, are considered in detail in this paper. For lasso-OLS the general representation leads to an estimateof the degrees of freedom based on the lasso solution path, which in turn can be used for estimating the risk of lasso-OLS.A similar estimate is proposed for best subset selection. The usefulness of the risk estimates for selecting the number of variablesis demonstrated via simulations with a particular focus on lasso-OLS.

AB - A representation of the degrees of freedom akin to Stein’s lemma is given for a class of estimators of a mean valueparameter in Rn. Contrary to previous results our representation holds for a range of discontinues estimators. It shows that eventhough the discontinuities form a Lebesgue null set, they cannot be ignored when computing degrees of freedom. Estimatorswith discontinuities arise naturally in regression if data driven variable selection is used. Two such examples, namely best subsetselection and lasso-OLS, are considered in detail in this paper. For lasso-OLS the general representation leads to an estimateof the degrees of freedom based on the lasso solution path, which in turn can be used for estimating the risk of lasso-OLS.A similar estimate is proposed for best subset selection. The usefulness of the risk estimates for selecting the number of variablesis demonstrated via simulations with a particular focus on lasso-OLS.

U2 - 10.1214/17-AIHP822

DO - 10.1214/17-AIHP822

M3 - Journal article

VL - 54

SP - 819

EP - 841

JO - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

SN - 0246-0203

IS - 2

ER -

ID: 197001906