Estimation of the distribution of random shifts deformation

Details Estimation of the distribution of random shifts deformation Estimation of the distribution of random shifts deformation

2008-12-17

arxiv.org/abs/0812.3253v1

Mathematics

Statistics Theory

Scientific paper

Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim is to construct a nonparametric estimator of the density of these random translation deformations using semiparametric preliminary estimates of the shifts. Building on results of Dalalyan et al. (2006), semiparametric estimators are obtained in our discrete framework and their performance studied. From these estimates we construct a nonparametric estimator of the target density. Both rates of convergence and an algorithm to construct the estimator are provided.

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