Nonparametric estimation of a renewal reward process from discrete data
vendredi 25 janvier 2013, 9h30 - 10h30
We study the nonparametric estimation of the jump density of a renewal reward process from the discrete observation of one trajectory over [0,T]. We consider the microscopic regime when the sampling rate tends to 0 as T goes to infinity. We propose an adaptive wavelet threshold density estimator and study its performance for the Lp loss, over Besov spaces. We achieve minimax rates of convergence for sampling rates that vanish with T at arbitrary polynomial rates. The estimation procedure is based on the inversion of the compounding operator. The inverse has no closed form expression and is approached with a fixed point technique.