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B-splines and discretization in an inverse problem for Poisson processes

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  • Szkutnik, Zbigniew

Abstract

Recent results on quasi-maximum likelihood histogram sieve estimators in inverse problems for Poisson processes are generalized to B-spline sieves. The impact of discretization effects on strong L2 consistency and convergence rates are studied in detail. In particular, a "rates saturation effect", caused by discretization, is demonstrated. Finite-sample implementation is proposed and tested in a Monte Carlo experiment with the Wicksell problem, which shows a superior performance of the new approach, when compared to other methods commonly used in that context. The proposed algorithm can also be used in cases with only approximately known folding kernel.

Suggested Citation

  • Szkutnik, Zbigniew, 2005. "B-splines and discretization in an inverse problem for Poisson processes," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 198-221, March.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:1:p:198-221
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    1. Szkutnik, Zbigniew, 2002. "A note on quasi-maximum likelihood solutions to an inverse problem for Poisson processes," Statistics & Probability Letters, Elsevier, vol. 60(3), pages 253-263, December.
    2. Szkutnik Z., 2003. "Doubly Smoothed EM Algorithm for Statistical Inverse Problems," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 178-190, January.
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