Volume 12, Issue 2, July 2013, Pages 145 - 151
Laws of the iterated logarithm for nonparametric sequential density estimators
Authors
Karima Lagha, Smail Adjabi
Corresponding Author
Karima Lagha
Received 6 June 2012, Accepted 5 February 2013, Available Online 15 July 2013.
- DOI
- 10.2991/jsta.2013.12.2.2How to use a DOI?
- Keywords
- Nonparametric density estimator, iterated logarithm, Parzen-Rosenblatt estimator, orthogonal polynomial estimator.
- Abstract
In this note, we establish a law of iterated logarithm for a triangular array of a random number of independent random variables and apply it to obtain laws of iterated logarithm for the sequential nonparametric density estimators. We consider the case of Rosenblatt-Parzen kernel estimators and orthogonal polynomial estimators. We point out that we obtain in the present paper sharp pointwise rates of the consistency.
- Copyright
- © 2013, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Karima Lagha AU - Smail Adjabi PY - 2013 DA - 2013/07/15 TI - Laws of the iterated logarithm for nonparametric sequential density estimators JO - Journal of Statistical Theory and Applications SP - 145 EP - 151 VL - 12 IS - 2 SN - 2214-1766 UR - https://doi.org/10.2991/jsta.2013.12.2.2 DO - 10.2991/jsta.2013.12.2.2 ID - Lagha2013 ER -