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FOURIER SERIES ESTIMATION FOR LENGTH BIASED DATA
Author(s) -
Jones M.C.,
Karunamuni R.J.
Publication year - 1997
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1997.tb00523.x
Subject(s) - estimator , fourier series , series (stratigraphy) , bhattacharyya distance , mean squared error , kernel density estimation , context (archaeology) , fourier transform , kernel (algebra) , mathematics , statistics , computer science , algorithm , mathematical analysis , artificial intelligence , geography , combinatorics , biology , paleontology , archaeology
summary This paper proposes and investigates Fourier series estimators for length biased data. Specifically, two Fourier series estimators are constructed and studied based on ideas of Jones (1991) and Bhattacharyya et al . (1988) in the case of kernel density estimation. Approximate expressions for mean squared errors and integrated mean squared errors are obtained and compared, and some simulated examples are investigated. The Fourier series estimator based on the proposal of Jones seems to have the more desirable properties of the two. The paper concludes with some comments that put this work in a wider context.