2018/12/04 by Piet Groeneboom, Groeneboom, Piet
Economics, Econometrics and Finance · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1812.01380
openalex publication_date 2018/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The finite-dimensional parameters of the monotone single index model are often estimated by minimization of a least squares criterion and reparametrization to deal with the non-unicity. We avoid the reparametrization by using a Lagrange-type method and replace the minimization over the finite-dimensional parameter alpha by a `crossing of zero' criterion at the derivative level. In particular, we consider a simple score estimator (SSE), an efficient score estimator (ESE), and a penalized least squares estimator (PLSE) for which we can apply this method. The SSE and ESE were discussed in Balabdaoui, Groeneboom and Hendrickx (2018, but the proofs still used reparametrization. Another version of the PLSE was discussed in Kuchibhotla and Patra (2017), where also reparametrization was used. The estimators are compared with the profile least squares estimator (LSE), Han's maximum rank estimator (MRE), the effective dimension reduction estimator (EDR) and a linear least squares estimator, which can be used if the covariates have an elliptically symmetric distribution. We also investigate the effects of random starting values in the search algorithms.