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Estimation in monotone single‐index models [PDF]
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.
Piet Groeneboom, Kim Hendrickx
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Let $(\bX, Y)$ be a random pair taking values in $\mathbb R^p \times \mathbb R$. In the so-called single-index model, one has $Y=f^{\star}(θ^{\star T}\bX)+\bW$, where $f^{\star}$ is an unknown univariate measurable function, $θ^{\star}$ is an unknown vector in $\mathbb R^d$, and $W$ denotes a random noise satisfying $\mathbb E[\bW|\bX]=0$.
Alquier, Pierre, Biau, Gérard
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Score Tests for the Single Index Model [PDF]
The single index model is a generalization of the linear regression model with E(y|x) = g(x′β), where g is an unknown function. The model provides a flexible alternative to the linear regression model while providing more structure than a fully nonparametric approach.
Jeffrey S. Simonoff, Chih-Ling Tsai
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On Single-Index Models beyond Gaussian Data
Sparse high-dimensional functions have arisen as a rich framework to study the behavior of gradient-descent methods using shallow neural networks, showcasing their ability to perform feature learning beyond linear models. Amongst those functions, the simplest are single-index models $f(x) = ϕ( x \cdot θ^*)$, where the labels are generated by an ...
Aaron Zweig +2 more
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A single-index quantile regression model and its estimation [PDF]
Models with single-index structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance. This paper focuses on a single-index model for the conditional quantile. We propose an adaptive
Xia, Y. +3 more
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Estimation of parametric single index ordered logit model on milk yields [PDF]
This article aims to determine some important factors affecting the milk yield of Holstein Friesian cows and introduce the use of single index ordered logit model in milk yield studies.
Özge AKKUŞ +3 more
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Penalized single-index quantile regression [PDF]
This article is made available through the Brunel Open Access Publishing Fund. Copyright for this article is retained by the author(s), with first publication rights granted to the journal.
Yu, K
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We study the non-parametric estimation of partially linear generalized single-index functional models, where the systematic component of the model has a flexible functional semi-parametric form with a general link function.
Mohamed Alahiane +3 more
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The Single-Index/Cox Mixture Cure Model [PDF]
AbstractIn survival analysis, it often happens that a certain fraction of the subjects under study never experience the event of interest, that is, they are considered “cured.” In the presence of covariates, a common model for this type of data is the mixture cure model, which assumes that the population consists of two subpopulations, namely the cured
Maïlis Amico +2 more
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Estimation of Single-Index Models Based on Boosting Techniques [PDF]
In single-index models the link or response function is not considered as fixed. The data determine the form of the unknown link function. In order to obtain a flexible form of the link function we specify the link function as an expansion in basis ...
Leitenstorfer, Florian, Tutz, Gerhard
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