2011/01/31 by Bernard Bercu, Philippe Fraysse
Computer Science · Mathematics · #Applied mathematics #Asymptotic analysis #Asymptotic distribution #Bayesian Methods and Mixture Models #Econometrics #Estimator #Kernel regression #Markov Chains and Monte Carlo Methods #Mathematics #Nonparametric regression #Nonparametric statistics #Parametric statistics #Regression #Regression analysis #Regression function #Semiparametric model #Semiparametric regression #Statistical Methods and Inference #Statistics #math.PR #math.ST #stat.TH
paper · pdf · doi:10.1214/12-aos969
published as Annals of Statistics 2012, Vol. 40, No. 2, 666-693 · Published in at http://dx.doi.org/10.1214/12-AOS969 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2012/04/01 · arxiv created 2012/06/04 · arxiv updated 2012/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins–Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins–Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya–Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins–Monro and Nadaraya–Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data.