Fourier series estimation for length biased data

Jones, M. C. and Karunamuni, R. J. (1997). Fourier series estimation for length biased data. Australian & New Zealand Journal of Statistics, 39(1) pp. 57–68.

DOI: https://doi.org/10.1111/j.1467-842X.1997.tb00523.x

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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