2016/12/31 by Tomas Mrkvicka, Tomáš Mrkvička, Mari Myllymaki +4 · 24 citations
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Analysis of variance #Envelope (radar) #Function (biology) #Functional data analysis #Interpretation (philosophy) #Local Government Finance and Decentralization #Null (SQL) #Null hypothesis #Regional Economics and Spatial Analysis #Spatial and Panel Data Analysis #Statistical hypothesis testing #stat.ME
paper · pdf · doi:10.14736/kyb-2020-3-0432
published in Kybernetika, 432-458 (Institute of Information Theory and Automation of the Czech Academy of Sciences) · arXiv admin note: text overlap with arXiv:1506.01646
openalex created_date 2017/01/06 · arxiv created 2020/05/22 · openalex publication_date 2020/07/14 · arxiv updated 2020/09/09 · openalex updated_date 2026/08/05
The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis is rejected with the predetermined significance level . The advantages of the proposed one-way functional ANOVA are that it identifies the domains of the functions which are responsible for the potential rejection. We introduce two versions of this test: the first gives a graphical interpretation of the test results in the original space of the functions and the second immediately offers a post-hoc test by identifying the significant pair-wise differences between groups. The proposed tests rely on discretization of the functions, therefore the tests are also applicable in the multidimensional ANOVA problem. In the empirical part of the article, we demonstrate the use of the method by analyzing fiscal decentralization in European countries.