2014/12/21 by E. Ostrovsky, Eugeny Ostrovsky, Ostrovsky, E. +2
Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Approximation and Integration #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1412.6829
arxiv created 2014/12/21 · openalex publication_date 2014/12/21 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of nonparametric estimation of the fractional derivative of unknown distribution function and of spectral function and show that these problems are well posed when the order of derivative is less than 0.5. We prove also the unbiaseness and asymptotical normality of offered estimates with optimal speed of convergence. For the construction of the confidence region in some functional norm we establish the Central Limit Theorem in correspondent Lebesgue-Riesz space for offered estimates, and deduce also the non-asymptotical deviation of our estimates in these spaces.