On a strongly consistent estimator of the squared L_2-norm of a function

Roman Różański

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 3, page 279-284
  • ISSN: 1233-7234

Abstract

top
A kernel estimator of the squared L 2 -norm of the intensity function of a Poisson random field is defined. It is proved that the estimator is asymptotically unbiased and strongly consistent. The problem of estimating the squared L 2 -norm of a function disturbed by a Wiener random field is also considered.

How to cite

top

Różański, Roman. "On a strongly consistent estimator of the squared L_2-norm of a function." Applicationes Mathematicae 23.3 (1995): 279-284. <http://eudml.org/doc/219131>.

@article{Różański1995,
abstract = {A kernel estimator of the squared $L_2$-norm of the intensity function of a Poisson random field is defined. It is proved that the estimator is asymptotically unbiased and strongly consistent. The problem of estimating the squared $L_2$-norm of a function disturbed by a Wiener random field is also considered.},
author = {Różański, Roman},
journal = {Applicationes Mathematicae},
keywords = {strong consistency; stochastic integral with respect to a p-parameter martingale; Poisson random field; Wiener random field; asymptotic unbiasedness; kernel estimator; stochastic integral with respect to a -parameter martingale; intensity function},
language = {eng},
number = {3},
pages = {279-284},
title = {On a strongly consistent estimator of the squared L\_2-norm of a function},
url = {http://eudml.org/doc/219131},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Różański, Roman
TI - On a strongly consistent estimator of the squared L_2-norm of a function
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 3
SP - 279
EP - 284
AB - A kernel estimator of the squared $L_2$-norm of the intensity function of a Poisson random field is defined. It is proved that the estimator is asymptotically unbiased and strongly consistent. The problem of estimating the squared $L_2$-norm of a function disturbed by a Wiener random field is also considered.
LA - eng
KW - strong consistency; stochastic integral with respect to a p-parameter martingale; Poisson random field; Wiener random field; asymptotic unbiasedness; kernel estimator; stochastic integral with respect to a -parameter martingale; intensity function
UR - http://eudml.org/doc/219131
ER -

References

top
  1. R. Cairoli and J. B. Walsh (1975), Stochastic integrals in the plane, Acta Math. 134, 111-183. Zbl0334.60026
  2. C. W. Gardiner (1984), Handbook for Stochastic Methods for Physics, Chemistry and the Natural Sciences, Springer Series in Synergetics, Berlin. 
  3. J. Koronacki and W. Wertz (1987), A global stopping rule for recursive density estimators, Statist. Planning Inference 20, 23-39. Zbl0850.62356
  4. H. Ramlau-Hansen (1983), Smoothing counting process intensities by means of kernel functions, Ann. Statist. 12, 453-466. Zbl0514.62050
  5. P. Reveš (1968), Laws of Large Numbers, Academic Press, New York. 
  6. R. Różański (1992), Recursive estimation of intensity function of a Poisson random field, J. Statist. Planning Inference 33, 165-174. Zbl0770.62084
  7. E. F. Schuster (1974), On the rate of convergence of an estimate of a probability density, Scand. Actuar. J., 103-107. Zbl0285.62016
  8.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.