Journal of Statistical Theory and Applications

Volume 12, Issue 2, August 2013, Pages 145 - 151

Laws of the iterated logarithm for nonparametric sequential density estimators

Authors
Karima Lagha, Smail Adjabi
Corresponding Author
Karima Lagha
Available Online 1 August 2013.
DOI
https://doi.org/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.
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This is an open access article distributed under the CC BY-NC license.

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
12 - 2
Pages
145 - 151
Publication Date
2013/08
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.2013.12.2.2How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Karima Lagha
AU  - Smail Adjabi
PY  - 2013
DA  - 2013/08
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  - https://doi.org/10.2991/jsta.2013.12.2.2
ID  - Lagha2013
ER  -