Autore
Salinelli, Ernesto

Titolo
Test of Normality based on Nonlinear Principal Components
Periodico
Università degli Studi del Piemonte Orientale 'A. Avogadro' : Facoltà di Economia - Dipartimento di Scienze Economiche e Metodi Quantitativi "SEMEQ" - Quaderni
Anno: 2009 - Fascicolo: 6 - Pagina iniziale: 1 - Pagina finale: 21

A new test of normality based on Nonlinear Principal Components (NLPC) is introduced. NLPC generalizes usual Linear Principal Components by considering the variance maximization problem over a general weighted Sobolev space of functions with an integrable first derivative. One obtains the following characterization of the normal law: among the distributions admitting NLPC, it is the unique for which the variance of the first NLPC is equal to the variance of the distribution. Our testing procedure uses this fine property i.e. testing normality is equivalent to testing for the equality between the first NLPC’s variance and the variance. The test statistic depends on a preliminary estimation of NLPC by orthonormal polynomials. The asymptotic distribution of the statistic is derived in case of known expectation and variance for strong mixing sequences of observations while a Monte Carlo method is used to approximate the distribution when these parameters are replaced by their empirical counterparts. We study the level and the power of the test for finite samples by means of a simulation experiment including a comparison with several other tests and some analysis of the effect of the degree of polynomials on the procedure.



Testo completo: http://semeq.unipmn.it/files/quaderno%20completo%206.pdf

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