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A Corrected Likelihood Approach for the Nonlinear Transformation Model with Application to Fluorescence Lifetime Measurements Using Exponential Mixtures

Author

Listed:
  • Rebafka Tabea

    (Institut Télécom, Télécom ParisTech (CNRS LTCI) and CEA, LIST)

  • Roueff François

    (Institut Télécom, Télécom ParisTech (CNRS LTCI))

  • Souloumiac Antoine

    (CEA, LIST)

Abstract

A fast and efficient estimation method is proposed that compensates the distortion in nonlinear transformation models. A likelihood-based estimator is developed that can be computed by an EM-type algorithm. The consistency of the estimator is shown and its limit distribution is provided. The new estimator is particularly well suited for fluorescence lifetime measurements, where only the shortest arrival time of a random number of emitted fluorescence photons can be detected and where arrival times are often modeled by a mixture of exponential distributions. The method is evaluated on real and synthetic data. Compared to currently used methods in fluorescence, the new estimator should allow a reduction of the acquisition time of an order of magnitude.

Suggested Citation

  • Rebafka Tabea & Roueff François & Souloumiac Antoine, 2010. "A Corrected Likelihood Approach for the Nonlinear Transformation Model with Application to Fluorescence Lifetime Measurements Using Exponential Mixtures," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-34, March.
    • Handle: RePEc:bpj:ijbist:v:6:y:2010:i:1:n:9
    DOI: 10.2202/1557-4679.1189
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    References listed on IDEAS

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    1. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(3), pages 295-313, December.
    2. A. Tsodikov, 2003. "Semiparametric models: a generalized self‐consistency approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 759-774, August.
    3. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
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