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

• Autorzy: Roman Różański
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

strong consistency; stochastic integral with respect to a p-parameter martingale; Poisson random field; Wiener random field; asymptotic unbiasedness; kernel estimator

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1995-1996
• Tom: 23
• Numer: 3
• Strony: 279-284

Daty

wydano

1995

otrzymano

1994-07-27

Twórcy

autor

Roman Różański

• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Bibliografia

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