2016/04/05 by Solesne Bourguin, Bourguin, Solesne, Claudio Durastanti +1
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Spectral Theory in Mathematical Physics #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1604.01316
openalex publication_date 2016/04/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this paper, quantitative central limit theorems for U-statistics on the\nq-dimensional torus defined in the framework of the two-sample problem for\nPoisson processes are derived. In particular, the U-statistics are built over\ntight frames defined by wavelets, named toroidal needlets, enjoying excellent\nlocalization properties in both harmonic and frequency domains. The\nBerry-Ess 'een type bounds associated with the normal approximations for these\nstatistics are obtained by means of the so-called Stein-Malliavin techniques on\nthe Poisson space, as introduced by Peccati, Sol 'e, Taqqu, Utzet (2011) and\nfurther developed by Peccati, Zheng (2010) and Bourguin, Peccati (2014).\nParticular cases of the proposed framework allow to consider the two-sample\nproblem on the circle as well as the local two-sample problem on \ℝq\nthrough a local homeomorphism argument.\n