Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes I

Journal of Statistical Theory and Applications (JSTA)

关键词: Divergence measures estimation;    Asymptotic normality;    Wavelet theory;    wavelets empirical processes;    Besov spaces;   

DOI  :  10.2991/jsta.2018.17.1.12

来源: DOAJ

【 摘 要 】

We deal with the normality asymptotic theory of empirical divergences measures based on wavelets in a series of three papers. In this first paper, we provide the asymptotic theory of the general of ϕ-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measures. Instead of using the Parzen nonparametric estimators of the probability density functions whose discrepancy is estimated, we use the wavelets approach and the geometry of Besov spaces. One-sided and two-sided statistical tests are derived. This paper is devoted to the foundations the general asymptotic theory and the exposition of the mains theoretical tools concerning the ϕ-forms, while proofs and next detailed and applied results will be given in the two subsequent papers which deal important key divergence measures and symmetrized estimators.

【 授权许可】

Unknown