caa a22 4500 477062989 CHVBK 20180405111406.0 cr unu---uuuuu 170330e19961201xx s 000 0 eng 10.1007/BF00052328 doi (NATIONALLICENCE)springer-10.1007/BF00052328 Estimation of a multivariate Box-Cox transformation to elliptical symmetry via the empirical characteristic function [Elektronische Daten] [Adolfo Quiroz, Miguel Nakamura, Francisco Pérez] Let X=(X 1, X 2,..., X d ) t be a random vector of positive entries, such that for some λ=(λ1,λ2,...,λ d ) t , the vector X (λ) defined by % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaamiwamaaDaaaleaamiaadMgaaSqaaWGaaiikaiabeU7aSnaaBaaa% baGaamyAaiaacMcaaeqaaaaakiabg2da9iaacIcadaWcgaqaaiaadI% fadaqhaaWcbaadcaWGPbaaleaamiabeU7aSnaaBaaabaGaamyAaaqa% baaaaOGaeyOeI0IaaGymaiaacMcaaeaacqaH7oaBdaWgaaWcbaadca% WGPbGaaiilaaWcbeaakiaadMgacqGH9aqpcaaIXaGaeSOjGSKaaiil% aiaadsgaaaaaaa!53BB!\[X_i^{(\lambda _{i)} } = ({{X_i^{\lambda _i } - 1)} \mathord{\left/ {\vphantom {{X_i^{\lambda _i } - 1)} {\lambda _{i,} i = 1 \ldots ,d}}} \right. \kern-\nulldelimiterspace} {\lambda _{i,} i = 1 \ldots ,d}}\]is elliptically symmetric. We describe a procedure based on the multivariate empirical characteristic function for estimating the λi's. Asymptotic results regarding consistency of the estimators are given and we evaluate their performance in simulated data. In a one-dimensional setting, comparisons are made with other available transformations to symmetry. The Institute of Statistical Mathematics, 1996 Elliptically contoured distributions nationallicence empirical characteristic function nationallicence Box-Cox transformations nationallicence Quiroz Adolfo Departmento de Matemáticas, Universidad Simón Bolívar, Apartado Postal 89000, Valle de Sartenejas, Baruta, Caracas, Venezuela aut Nakamura Miguel Centro de Investigación en Matemáticas, Apartado Postal 402, 36000, Guanajuato, Gto., Mexico aut Pérez Francisco Centro de Investigación en Matemáticas, Apartado Postal 402, 36000, Guanajuato, Gto., Mexico aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/4(1996-12-01), 687-709 0020-3157 48:4<687 1996 48 10463 https://doi.org/10.1007/BF00052328 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00052328 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Quiroz Adolfo Departmento de Matemáticas, Universidad Simón Bolívar, Apartado Postal 89000, Valle de Sartenejas, Baruta, Caracas, Venezuela aut NATIONALLICENCE 700 1- Nakamura Miguel Centro de Investigación en Matemáticas, Apartado Postal 402, 36000, Guanajuato, Gto., Mexico aut NATIONALLICENCE 700 1- Pérez Francisco Centro de Investigación en Matemáticas, Apartado Postal 402, 36000, Guanajuato, Gto., Mexico aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/4(1996-12-01), 687-709 0020-3157 48:4<687 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer