SEMIPARAMETRIC MIXTURES FOR BACKGROUND DENSITY ESTIMATION IN PARTICLE PHYSICS

The work in this thesis aims to develop a method to estimate the density of events in particle physics experiments, through a semiparametric mixture of a known parametric “signal” density and an unknown nonparametric “background” density. This method relies on an assumption of local smoothness of the background around the signal. The nonparametric component is estimated with a local orthogonal polynomial expansion (LOrPE), the level of overall smoothness of which is selected through a local version of least squares cross-validation. The estimate of the background is constructed iteratively through weighting of the original signal and background sample. The mixing proportion is chosen via maximum penalized local likelihood and the penalization term is a representation of the local complexity. This term is obtained with a novel estimator of the effective degrees of freedom, that relies on rejection sampling to localize the variability of the data around the interest region. Simulation studies show how the procedure operates, in its local version and in the global one, which is also presented.