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On parametric density estimators

Published online by Cambridge University Press:  01 July 2016

C. R. Heathcote
C. R. Heathcote*
Affiliation:
The Australian National University, Canberra
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Extract

There is an extensive literature on estimating a probability density (or some other appropriate curve) f using statistics of the form Here X 1, X 2, · · ·, Xn is a sample from the population, the weight function w is constrained by suitable regularity conditions, and the sequence {bn } of band-widths satisfies bn → 0, nbn → ∞ as n → ∞. Rosenblatt (1971) presents details of this method of estimation and provides an extensive list of references.

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 4 , December 1978 , pp. 735 - 740
Copyright
Copyright © Applied Probability Trust 1978 

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References

Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H. and Tukey, J. W. (1972) Robust Estimates of Location. Princeton University Press.Google Scholar
Beran, R. (1977) Minimum Hellinger distance estimates for parametric models. Ann. Statist. 3, 445–463.Google Scholar
Heathcote, C. R. (1977) The integrated squared error estimation of parameters. Biometrika 64, 255–264.Google Scholar
Huber, P. J. (1972) Robust statistics; a review. Ann. Math. Statist. 43, 1041–1067.CrossRefGoogle Scholar
Pickands, J. (1969) Efficient estimation of a probability density function. Ann. Math. Statist. 40, 854–864.Google Scholar
Rosenblatt, M. (1971) Curve estimates. Ann. Math. Statist. 42, 1815–1842.Google Scholar