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Date
2024Type
- Journal Article
ETH Bibliography
yes
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Abstract
The distributional single index model is a semiparametric regression model in which the conditional distribution functions P(Y ≤ y | X = x) = F₀(θ₀(x), y) of a real-valued outcome variable Y depend on d-dimensional covariates X through a univariate, parametric index function θ₀(x), and increase stochastically as θ₀(x) increases. We propose least squares approaches for the joint estimation of θ₀ and F₀ in the important case where θ₀(x) = αᵀ₀x and obtain convergence rates of n⁻¹/³, thereby improving an existing result that gives a rate of n⁻¹/⁶. A simulation study indicates that the convergence rate for the estimation of α₀ might be faster. Furthermore, we illustrate our methods in an application on house price data that demonstrates the advantages of shape restrictions in single index models. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000667298Publication status
publishedExternal links
Journal / series
Statistica NeerlandicaPublisher
Wiley-BlackwellSubject
monotone regression; isotonic distributional regression; single index modelMore
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ETH Bibliography
yes
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