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Estimation in monotone single-index models. / Groeneboom, Piet; Hendrickx, Kim.

In: Statistica Neerlandica, 2018, p. 1-22.

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Groeneboom, P & Hendrickx, K 2018, 'Estimation in monotone single-index models', Statistica Neerlandica, pp. 1-22. https://doi.org/10.1111/stan.12138

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Groeneboom, Piet ; Hendrickx, Kim. / Estimation in monotone single-index models. In: Statistica Neerlandica. 2018 ; pp. 1-22.

BibTeX

@article{c95c8eb3c91e4831b2585e59f102c1e5,
title = "Estimation in monotone single-index models",
abstract = "Single-index models are popular regression models that are more flexible than linear models and still maintain more structure than purely nonparametric models. We consider the problem of estimating the regression parameters under a monotonicity constraint on the unknown link function. In contrast to the standard approach of using smoothing techniques, we review different {"}non-smooth{"} estimators that avoid the difficult smoothing parameter selection. For about 30 years, one has had the conjecture that the profile least squares estimator is an n-consistent estimator of the regression parameter, but the only non-smooth argmin/argmax estimators that are actually known to achieve this n-rate are not based on the nonparametric least squares estimator of the link function. However, solving a score equation corresponding to the least squares approach results in n-consistent estimators. We illustrate the good behavior of the score approach via simulations. The connection with the binary choice and current status linear regression models is also discussed.",
keywords = "Least squares, Monotone link function, Single-index model",
author = "Piet Groeneboom and Kim Hendrickx",
year = "2018",
doi = "10.1111/stan.12138",
language = "English",
pages = "1--22",
journal = "Statistica Neerlandica",
issn = "0039-0402",
publisher = "Blackwell",

}

RIS

TY - JOUR

T1 - Estimation in monotone single-index models

AU - Groeneboom, Piet

AU - Hendrickx, Kim

PY - 2018

Y1 - 2018

N2 - Single-index models are popular regression models that are more flexible than linear models and still maintain more structure than purely nonparametric models. We consider the problem of estimating the regression parameters under a monotonicity constraint on the unknown link function. In contrast to the standard approach of using smoothing techniques, we review different "non-smooth" estimators that avoid the difficult smoothing parameter selection. For about 30 years, one has had the conjecture that the profile least squares estimator is an n-consistent estimator of the regression parameter, but the only non-smooth argmin/argmax estimators that are actually known to achieve this n-rate are not based on the nonparametric least squares estimator of the link function. However, solving a score equation corresponding to the least squares approach results in n-consistent estimators. We illustrate the good behavior of the score approach via simulations. The connection with the binary choice and current status linear regression models is also discussed.

AB - Single-index models are popular regression models that are more flexible than linear models and still maintain more structure than purely nonparametric models. We consider the problem of estimating the regression parameters under a monotonicity constraint on the unknown link function. In contrast to the standard approach of using smoothing techniques, we review different "non-smooth" estimators that avoid the difficult smoothing parameter selection. For about 30 years, one has had the conjecture that the profile least squares estimator is an n-consistent estimator of the regression parameter, but the only non-smooth argmin/argmax estimators that are actually known to achieve this n-rate are not based on the nonparametric least squares estimator of the link function. However, solving a score equation corresponding to the least squares approach results in n-consistent estimators. We illustrate the good behavior of the score approach via simulations. The connection with the binary choice and current status linear regression models is also discussed.

KW - Least squares

KW - Monotone link function

KW - Single-index model

UR - http://www.scopus.com/inward/record.url?scp=85045883593&partnerID=8YFLogxK

UR - http://resolver.tudelft.nl/uuid:c95c8eb3-c91e-4831-b258-5e59f102c1e5

U2 - 10.1111/stan.12138

DO - 10.1111/stan.12138

M3 - Article

AN - SCOPUS:85045883593

SP - 1

EP - 22

JO - Statistica Neerlandica

JF - Statistica Neerlandica

SN - 0039-0402

ER -

ID: 44972571