Niveau: Supérieur, Doctorat, Bac+8
Estimation of the distribution of random shifts deformation I. Castillo & J-M. Loubes Abstract Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribu- tion µ, modeling the variability in the response of each individual. Our aim is to construct a nonparametric estimator of the density of these random translation de- formations using semiparametric preliminary estimates of the shifts. Building on results of Dalalyan et al. (2006), semiparametric estimators are obtained in our dis- crete 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. Keywords: Semiparametric statistics, Order two properties, Penalized Maximum Likelihood, Practical algorithms. Subject Class. MSC-2000: 62G05, 62G20. 1 Introduction Our aim is to estimate the common density ? of independent random variables ?j , j = 1, . . . , Jn, with distribution µ, observed in a panel data analysis framework in a translation model. More precisely, consider Jn unknown curves t ? f [j](t) sampled at multiple points tij = ti = i/n, i = 1, . . . , n, with random i.i.d. translation effects ?j , j = 1, .
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