Statistical properties of amplitude and decay parameter estimators for fluorescence lifetime imaging

We analyze the statistical properties of the maximum likelihood estimator, least squares estimator, and Pearson's χ²-based and Neyman's χ²-based estimators for the estimation of decay constants and amplitudes for fluorescence lifetime imaging. Our analysis is based on the linearization of the gradient of the objective functions around true parameters. The analysis shows that only the maximum likelihood estimator based on the Poisson likelihood function yields unbiased and efficient estimation. All other estimators yield either biased or inefficient estimations. We validate our analysis by using simulations.