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 R and the response is scalar. The response is modelled as Y=WðXÞ+e, where W is some linear continuous operator defined on the space of square integrable functions and valued in R R. The random input X is independent from the noise e. In this paper, we are interested in testing the null hypothesis of no effect, that is, the nullity of W 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 v 2 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.

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The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a slight modification of the usual penalty. Theoretical analysis concentrates on the error in an out-of-sample prediction of the response for a new random function $X_{n+1}$. It is shown that rates of convergence of the prediction error depend on the smoothness of the slope function and on the structure of the predictors. We then prove that these rates are optimal in the sense that they are minimax over large classes of possible slope functions and distributions of the predictive curves. For the case of models with errors-in-variables the smoothing spline estimator is modified by using a denoising correction of the covariance matrix of discretized curves. The methodology is then applied to a real case study where the aim is to predict the maximum of the concentration of ozone by using the curve of this concentration measured the preceding day.Comment: Published in at http://dx.doi.org/10.1214/07-AOS563 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Summary:Iron overload is associated with free radical generation and tissue damage. Our main objective was to ascertain the frequency and severity of iron overload in a group of 59 patients who died after conventional-intensity autologous (n ¼ 24) or allogeneic (n ¼ 35) haematopoietic stem cell transplantation (HSCT). A second objective was to investigate associations between liver-iron concentration and causes of transplant-related mortality. The median age was 41 years (range, 19-66), 41 were males and 18 females. In total, 26 patients had acute leukaemia or MDS, 10 CML, 17 lymphoma, four myeloma and two aplastic anaemia. The median hepatic iron concentration (HIC) was 138 lmol/g dry weight (7.7 mg/g; range 31-631 lmol/g). In total, 4/32 (12%) patients with HIC o150 lmol/g and 10/27 (37%) with hepatic iron X150 lmol/g showed invasive aspergillosis at autopsy (P ¼ 0.035). This was significant in multivariate analysis (RR 9.0; 95% CI 1.6-50.3, P ¼ 0.012). In conclusion, severe iron overload is frequent in patients who die following HSCT and is associated with invasive aspergillosis.