2018/07/31 by H.-P. Dembinski, Hans Dembinski, M. Schmelling +2
Decision Sciences · Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Algorithm #Applied mathematics #Discrete mathematics #Equivalence (formal languages) #Estimation theory #Generalized least squares #Iterated function #Least-squares function approximation #Mathematical analysis #Mathematical optimization #Mathematics #Non-linear least squares #Optimal Experimental Design Methods #Simple (philosophy) #Statistical Methods and Bayesian Inference #Statistics #hep-ex #physics.data-an #stat.AP
paper · pdf · doi:10.1016/j.nima.2019.05.086
Accepted by NIMA
openalex publication_date 2019/05/29 · arxiv created 2019/06/06 · arxiv updated 2019/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the well known fact that commonly used variants of the least-squares fit applied to Poisson-distributed data produce biased estimates. The bias can be overcome with an iterated weighted least-squares method, which produces results identical to the maximum-likelihood method. For linear models, the iterated weighted least-squares method converges faster than the equivalent maximum-likelihood method, and does not require problem-specific starting values, which may be a practical advantage. The equivalence of both methods also holds for binomially distributed data. We further show that the unbinned maximum-likelihood method can be derived as a limiting case of the iterated least-squares fit when the bin width goes to zero, which demonstrates a deep connection between the two methods.