2020/05/22 by Valentin Konakov, Konakov, Valentin, Vladimir Panov +3
Economics, Econometrics and Finance · Mathematics · #60G15 #60G70 #62G07 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Methods and Inference #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2005.11249
openalex publication_date 2020/05/22 · openalex created_date 2020/05/29 · openalex updated_date 2026/07/28
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main theorem yields the asymptotic representation of the corresponding distribution function with exponentially decaying remainder term. This result can be efficiently used for studying the projection density estimates, based, for instance, on Legendre polynomials. More precisely, we construct the sequence of accompanying laws, which approximates the distribution of maximal deviation of the considered estimates with polynomial rate. Moreover, we construct the confidence bands for densities, which are honest at polynomial rate to a broad class of densities.