On Misspecification Estimation in Monotone Single-Index Models  
Author Fadoua Balabdaoui

 
Co-Author(s) Cécile Durot; Christopher Fragneau

 
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.

 
Keywords De-spasified Lasso, High dimension, Misspecified model, Monotone single-index model
   
    Article #:  DSBFI23-72
 
Proceedings of 2nd ISSAT International Conference on Data Science in Business, Finance and Industry
January 8-10, 2023 - Da Nang, Vietnam