Mathematical Methods of Statistics

, Volume 26, Issue 2, pp 81–110 | Cite as

Moment convergence in regularized estimation under multiple and mixed-rates asymptotics

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Abstract

In M-estimation under standard asymptotics, the weak convergence combined with the polynomial type large deviation estimate of the associated statistical random field Yoshida (2011) provides us with not only the asymptotic distribution of the associated M-estimator but also the convergence of its moments, the latter playing an important role in theoretical statistics. In this paper, we study the above program for statistical random fields of multiple and also possibly mixedrates type in the sense of Radchenko (2008) where the associated statistical random fields may be nondifferentiable and may fail to be locally asymptotically quadratic. Consequently, a very strong mode of convergence of a wide range of regularized M-estimators is ensured.Our results are applied to regularized estimation of an ergodic diffusion observed at high frequency.

Keywords

regularized estimation moment convergence large deviation inequality sparse estimation stochastic differential equation mixed-rates asymptotics 

2000 Mathematics Subject Classification

62E20 

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Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Faculty of Math.Kyushu Univ.FukuokaJapan
  2. 2.Dept.Math.Josai Univ.SakadoJapan

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