Abstract: We propose a nonparametric density estimator based on data that are repeatedly observed with independent measurement errors. We particularly focus on cases where the Fourier transform of the error density has some zeros and shows oscillations. Our estimator attains the same rates of convergence as obtains under smooth error densities whose Fourier transform have the corresponding tails but no zeros. We prove minimax results for estimating the distribution function and for support estimation in the same model. A simulation study supports our findings.
Key words and phrases: Analysis of variance, characteristic function, components of variance, deconvolution, nonparametric density estimation, panel data, repeated measurements.