Sequential Model Selection Method for Nonparametric Autoregression

In this paper for the first time the nonparametric autoregression estimation problem for the quadratic risks is considered. To this end we develop a new adaptive sequential model selection method based on the efficient sequential kernel estimators proposed by Arkoun and Pergamenshchikov (2016). Moreover, we develop a new analytical tool for general regression models to obtain the non asymptotic sharp or- acle inequalities for both usual quadratic and robust quadratic risks. Then, we show that the constructed sequential model selection proce- dure is optimal in the sense of oracle inequalities.Comment: 30 page

Estimation séquentielle pour modèles autorégressifs

International audienc

Estimation non paramétrique pour des modèles de diffusion et de régression

Pas de résuméPas de résum

Estimation non paramétrique pour des modèles de diffusion et de régression

STRASBOURG-Sc. et Techniques (674822102) / SudocSudocFranceF

Adaptive efficient robust sequential analysis for autoregressive big data models *

In this paper we consider high dimension models based on dependent observations defined through autoregressive processes. For such models we develop an adaptive efficient estimation method via the robust sequential model selection procedures. To this end, we first obtain a van Trees inequality for such models, and then, using this inequality, we probably for the first time obtain a sharp lower bound for the weighted robust risk in an explicit form given by the famous Pinsker constant. Moreover, in getting this lower bound we have found the nonparametric version of the Fisher information for this model. Then, using the weighted least square method and sharp non asymptotic oracle inequalities from (Arkoun O., Brua J.-Y., and Pergamenchtchikov S. 2019. Sequential Analysis 38(4): 437-460), we develop analytic tools to provide the efficiency property in the minimax sense for the proposed estimation procedure, i.e. we show that the upper bound for its risk coincides with the obtained lower bound. It should be emphasized that this property is obtained without using sparse conditions and in the adaptive setting when the parameter dimension and model regularity are unknown. We then study the constructed procedures numerically using Monte Carlo simulations

Sequential Model Selection Method for Nonparametric Autoregression

International audienceIn this paper for the first time the nonparametric autoregression estimation problem for the quadratic risks is considered. To this end we develop a new adaptive sequential model selection method based on the efficient sequential kernel estimators proposed by Arkoun and Pergamenshchikov (2016). Moreover, we develop a new analytical tool for general regression models to obtain the non asymptotic sharp oracle inequalities for both usual quadratic and robust quadratic risks. Then, we show that the constructed sequential model selection procedure is optimal in the sense of oracle inequalities

Sequential Model Selection Method for Nonparametric Autoregression

In this paper for the first time the nonparametric autoregression estimation problem for the quadratic risks is considered. To this end we develop a new adaptive sequential model selection method based on the efficient sequential kernel estimators proposed by Arkoun and Pergamenshchikov (2016). Moreover, we develop a new analytical tool for general regression models to obtain the non asymptotic sharp oracle inequalities for both usual quadratic and robust quadratic risks. Then, we show that the constructed sequential model selection procedure is optimal in the sense of oracle inequalities. MSC: primary 62G08, secondary 62G0

Estimation séquentielle pour modèles autorégressifs

International audienc

Adaptive efficient robust estimation for nonparametric autoregressive models

In this paper for the first time the adaptive efficient estimation problem for nonparametric autoregressive models has been studied. First of all, through the Van Trees inequality the sharp bound for the robust quadratic risks, i.e. the Pinsker constant (see, for example , in [19]), in explicit form has been obtained. Then, through the sharp oracle inequalities method developed in [4] for non parametric autoregressions an adaptive efficient model selection procedure is proposed , i.e. such for which the upper bound of its robust quadratic risk coincides with the obtained Pinsker constant. MSC: primary 62G08, secondary 62G0