FOURIER SERIES ESTIMATION FOR LENGTH BIASED DATA |
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| Authors: | M.C. Jones R.J. Karunamuni |
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| Affiliation: | Dept of Statistics, The Open University, Milton Keynes MK7 6AA, UK.;Dept of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1. |
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| Abstract: | 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. |
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| Keywords: | Density estimation length biased data Fourier series mean squared error integrated mean squared error |
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