International Society of Science and Applied Technologies |
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On Misspecification Estimation in Monotone Single-Index Models | ||||
Author | Fadoua Balabdaoui
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Co-Author(s) | Cécile Durot; Christopher Fragneau
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Abstract | We study the monotone single index model in a high dimensional context. This model assumes that a real response variable Y is linked to a d dimensional covariate X through the relationship E[Y |X] = Ψ0(αT0 X) a.s. Both the ridge function Ψ0 and the index parameter α0 are unknown and the ridge function is assumed to be monotone. Moreover, we will assume that d depends on the number of observations and X is assumed to be a Gaussian vector. We propose an estimator of the index based on a misspecification procedure and we derive estimators of the bundled function Ψ0(αT0 ・) and the isolated ridge regression Ψ0. Under some appropriate conditions, we get a parametric rate of convergence for the index and the rate of convergence in the L2 norm of the bundled function and the ridge function.
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Keywords | De-spasified Lasso, High dimension, Misspecified model, Monotone single-index model | |||
Article #: DSBFI23-72 |
January 8-10, 2023 - Da Nang, Vietnam |