Adaptive efficient estimation for generalized semi-Markov big data models

被引：0
作者：
Vlad Stefan Barbu
Slim Beltaief
Serguei Pergamenchtchikov
机构：
[1] Laboratoire de Mathématiques Raphaël Salem,International Laboratory of Statistics of Stochastic Processes and Quantitative Finance
[2] UMR 6085 CNRS-Université de Rouen Normandie,undefined
[3] ALTEN de Toulouse,undefined
[4] Tomsk State University,undefined
来源：
Annals of the Institute of Statistical Mathematics | 2022年 / 74卷
关键词：
Regression model; Generalized semi-Markov processes; Fractional Poisson processes; Non-asymptotic estimation; Robust estimation; Model selection; Sharp oracle inequalities; Asymptotic efficiency; Adaptive estimation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we study generalized semi-Markov high dimension regression models in continuous time, observed at fixed discrete time moments. The generalized semi-Markov process has dependent jumps and, therefore, it is an extension of the semi-Markov regression introduced in Barbu et al. (Stat Inference Stoch Process 22:187–231, 2019a). For such models we consider estimation problems in nonparametric setting. To this end, we develop model selection procedures for which sharp non-asymptotic oracle inequalities for the robust risks are obtained. Moreover, we give constructive sufficient conditions which provide through the obtained oracle inequalities the adaptive robust efficiency property in the minimax sense. It should be noted also that, for these results, we do not use neither sparse conditions nor the parameter dimension in the model. As examples, regression models constructed through spherical symmetric noise impulses and truncated fractional Poisson processes are considered. Numerical Monte-Carlo simulations confirming the theoretical results are given in the supplementary materials.
引用
收藏
页码：925 / 955
页数：30
相关论文
共 32 条
  • [1] Barbu VS(2019)Robust adaptive efficient estimation for semi-Markov nonparametric regression models Statistical Inference for Stochastic Processes 22 187-231
  • [2] Beltaief S(2019)Robust statistical signal processing in semi-Markov nonparametric regression models Les Annales de l’I.S.U.P 63 45-56
  • [3] Pergamenshchikov SM(2020)Model selection for the robust efficient signal processing observed with small Lévy noise Annals of the Institute of Statistical Mathematics 72 1205-1235
  • [4] Barbu VS(2001)Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial mathematics Journal of the Royal Statistical Society Series B (Statistical Methodology) 63 167-241
  • [5] Beltaief S(2014)Fractional Poisson processes: Long-range dependence and applications in ruin theory Journal of Applied Probability 51 727-740
  • [6] Pergamenshchikov SM(2007)Improved selection model method for the regression with dependent noise Annals of the Institute of Statistical Mathematics 59 435-464
  • [7] Beltaief S(2019)The Dantzig selector for a linear model of diffusion processes Statistical Inference for Stochastic Processes 22 475-498
  • [8] Chernoyarov O(2009)Nonparametric estimation in a semimartingale regression model. Par.t 1. Oracle Inequalities Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika 3 23-41
  • [9] Pergamenshchikov SM(2009)Nonparametric estimation in a semimartingale regression model. Part 2. Robust asymptotic efficiency Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika 4 31-45
  • [10] Barndorff-Nielsen OE(2012)Efficient robust nonparametric in a semimartingale regression model Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 48 1217-1244
1234