Limit distributions for asymptotically linear statistics with spherical error
AbstractThe aim of this work is to obtain general results for the limit distributions of asymptotically linear statistics when the error is spherical, increasing non-centrality. These results apply directly to homoscedastic normal error thus to high precision measurements. We present a numerical example on cylinder volume to illustrate the usefulness of our approach.
C. Fernandez, J. Osiewalski, M. Steel, Modelling & inference with ν-spherical distributions. J. Amer. Statist. Assoc., vol. 90, no. 432, pp 1331 – 1340, 1995.
D. Ferreira, S.S Ferreira, C. Nunes, L. Ramos and J.T. Mexia, Approximate normality of low degree polynomials in normal independent variables. Far East J. Math. Sci., vol. 68, no. 2, pp. 287 - 296, 2012.
D. Ferreira, S.S. Ferreira, C. Nunes and S. Incio, Inducing pivot variables and non-centrality parameters in elliptical distributions. 11th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc., vol. 1558, pp. 833-836, 2013.
D. Ferreira, S.S. Ferreira, C. Nunes, M. Fonseca and J.T. Mexia, Chisquared and Related Inducing Pivot Variables: An Application to Orthogonal Mixed Models, Communications in Statistics - Theory and Methods, 2013. doi:10.1080/03610926.2013.770532
M. Loeve, Probability Theory, 4th ed., New York, NY: Springer, 1977.
J.T. Mexia and M.M. Oliveira, Asymptotic linearity and limit distributions, approximations. J. Stat. Plan. Infer., vol. 140, no. 2, pp. 353-357, 2010.
J.T. Mexia, C. Nunes and M.M. Oliveira, Multivariate Application Domains for the Delta Method. In Proceedings of 9th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. vol. 1389, pp. 1486-1489, 2011.
C. Nunes, M.M. Oliveira and J.T. Mexia, Application domains for the Delta method. Statistics, vol. 47, no. (2), pp. 317-328, 2013.
R.N. Rattihalli and P.Y. Patil, Generalized υ-Spherical Densities. Communications in Statistics - Theory and Methods, vol. 39, no. 19, pp. 3568-3583, 2013.
M.M. Oliveira,Modelacao de séries emparelhadas de estudos com estrutura comum. Unpublished PhD thesis, Universidade deÉvora,2002.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).