Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

ASYMPTOTIC THEORY OF SEMIPARAMETRIC Z -ESTIMATORS FOR STOCHASTIC PROCESSES WITH APPLICATIONS TO ERGODIC DIFFUSIONS AND TIME SERIES

Yoichi Nishiyama
The Annals of Statistics
Vol. 37, No. 6A (December 2009), pp. 3555-3579
Stable URL: http://www.jstor.org/stable/25662203
Page Count: 25
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
ASYMPTOTIC THEORY OF SEMIPARAMETRIC
              Z
              -ESTIMATORS FOR STOCHASTIC PROCESSES WITH APPLICATIONS TO ERGODIC DIFFUSIONS AND TIME SERIES
Preview not available

Abstract

This paper generalizes a part of the theory of Z-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to derive the asymptotic behavior of the solution to an estimating equation $\theta \rightsquigarrow \Psi _{n}(\theta,\hat{h}_{n})=0$ with an abstract nuisance parameter h when the compensator of Ψ n is random. As its application, we consider the estimation problem in an ergodic diffusion process model where the drift coefficient contains an unknown, finite-dimensional parameter θ and the diffusion coefficient is indexed by a nuisance parameter h from an infinite-dimensional space. An example for the nuisance parameter space is a class of smooth functions. We establish the asymptotic normality and efficiency of a Z-estimator for the drift coefficient. As another application, we present a similar result also in an ergodic time series model.

Page Thumbnails

  • Thumbnail: Page 
3555
    3555
  • Thumbnail: Page 
3556
    3556
  • Thumbnail: Page 
3557
    3557
  • Thumbnail: Page 
3558
    3558
  • Thumbnail: Page 
3559
    3559
  • Thumbnail: Page 
3560
    3560
  • Thumbnail: Page 
3561
    3561
  • Thumbnail: Page 
3562
    3562
  • Thumbnail: Page 
3563
    3563
  • Thumbnail: Page 
3564
    3564
  • Thumbnail: Page 
3565
    3565
  • Thumbnail: Page 
3566
    3566
  • Thumbnail: Page 
3567
    3567
  • Thumbnail: Page 
3568
    3568
  • Thumbnail: Page 
3569
    3569
  • Thumbnail: Page 
3570
    3570
  • Thumbnail: Page 
3571
    3571
  • Thumbnail: Page 
3572
    3572
  • Thumbnail: Page 
3573
    3573
  • Thumbnail: Page 
3574
    3574
  • Thumbnail: Page 
3575
    3575
  • Thumbnail: Page 
3576
    3576
  • Thumbnail: Page 
3577
    3577
  • Thumbnail: Page 
3578
    3578
  • Thumbnail: Page 
3579
    3579