Testing Hypotheses in the Functional Linear Model Export

@article{citeulike:4114157, abstract = {The functional linear model with scalar response is a regression model where the predictor is a random function defined on some compact set of R and the response is scalar. The response is modelled as Y=03A8(X)+025B, where 03A8 is some linear continuous operator defined on the space of square integrable functions and valued in R. The random input X is independent from the noise 025B. In this paper, we are interested in testing the null hypothesis of no effect, that is, the nullity of 03A8 restricted to the Hilbert space generated by the random variable X. We introduce two test statistics based on the norm of the empirical cross-covariance operator of (X,Y). The first test statistic relies on a 03C72 approximation and we show the asymptotic normality of the second one under appropriate conditions on the covariance operator of X. The test procedures can be applied to check a given relationship between X and Y. The method is illustrated through a simulation study.}, address = {Unit Biomtrie et Intelligence Artificielle, INRA Toulouse. ; GRIMM, Universit Toulouse Le Mirail. ; CREST-INSEE et Laboratoire de Statistique et Probabilits, Universit Paul Sabatier. ; Laboratoire de Statistique et Probabilits, Universit Paul Sabatier.}, author = {Cardot, Herv\'{e} and Ferraty, Fr\'{e}d\'{e}ric and Mas, Andr\'{e} and Sarda, Pascal}, citeulike-article-id = {4114157}, citeulike-linkout-0 = {http://dx.doi.org/10.1111/1467-9469.00329}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/118839367/ABSTRACT}, doi = {10.1111/1467-9469.00329}, journal = {Scandinavian Journal of Statistics}, keywords = {cmg, forclass, nsf}, number = {1}, pages = {241--255}, posted-at = {2009-02-27 20:04:24}, priority = {2}, title = {Testing Hypotheses in the Functional Linear Model}, url = {http://dx.doi.org/10.1111/1467-9469.00329}, volume = {30}, year = {2003} }

TY - JOUR ID - citeulike:4114157 L3 - citeulike-article-id:4114157 N2 - The functional linear model with scalar response is a regression model where the predictor is a random function defined on some compact set of R and the response is scalar. The response is modelled as Y=03A8(X)+025B, where 03A8 is some linear continuous operator defined on the space of square integrable functions and valued in R. The random input X is independent from the noise 025B. In this paper, we are interested in testing the null hypothesis of no effect, that is, the nullity of 03A8 restricted to the Hilbert space generated by the random variable X. We introduce two test statistics based on the norm of the empirical cross-covariance operator of (X,Y). The first test statistic relies on a 03C72 approximation and we show the asymptotic normality of the second one under appropriate conditions on the covariance operator of X. The test procedures can be applied to check a given relationship between X and Y. The method is illustrated through a simulation study. IS - 1 JF - Scandinavian Journal of Statistics AD - Unit Biomtrie et Intelligence Artificielle, INRA Toulouse. ; GRIMM, Universit Toulouse Le Mirail. ; CREST-INSEE et Laboratoire de Statistique et Probabilits, Universit Paul Sabatier. ; Laboratoire de Statistique et Probabilits, Universit Paul Sabatier. EP - 255 TI - Testing Hypotheses in the Functional Linear Model VL - 30 SP - 241 KW - cmg KW - forclass KW - nsf AU - Cardot, Hervé AU - Ferraty, Frédéric AU - Mas, André AU - Sarda, Pascal PY - 2003/// UR - http://dx.doi.org/10.1111/1467-9469.00329 ER -