Functional linear regression via canonical analysis

We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of functional linear regression analysis. A specific procedure for the estimation of the regression parameter function using canonical expansions is proposed and compared with an established functional principal component regression approach. As an example of an application, we present an analysis of mortality data for cohorts of medflies, obtained in experimental studies of aging and longevity.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ228 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Biomarkers of Inflammation and Fibrosis in Kawasaki Disease Patients Years After Initial Presentation With Low Ejection Fraction.

Background Coronary artery aneurysms and myocarditis are well-recognized complications of Kawasaki disease (KD) but no systematic evaluation of the consequences of myocarditis has been performed in the subset presenting with low ejection fraction (EF). We postulated that more severe myocardial inflammation as evidenced by low EF during the acute phase could lead to late myocardial fibrosis. Methods and Results We measured the carboxyterminal propeptide of procollagen type I (PIPC), soluble suppressor of tumorigenicity 2, galectin-3 (Gal-3), growth-differentiation factor-15, and calprotectin by ELISA in late convalescent blood samples from 16 KD patients who had an EF ≤55% on their initial echocardiogram. Results were compared with samples from sex- and age-matched KD patients with initial EF >60%. In the univariate analysis, the median Gal-3 and PIPC levels in the low EF group were significantly higher than those in the normal EF group (Gal-3: low EF 6.216 versus normal EF 4.976 mg/dL P=0.038, PIPC: low EF 427.4 versus normal EF 265.2 mg/dL, P=0.01). In a multivariable analysis, there were significant differences for Gal-3 and PIPC levels between the low and normal EF groups, adjusting for age, sex, and worst z score. Conclusions Convalescent KD patients with a history of low EF during the acute illness had significantly elevated levels of Gal-3 and PIPC when compared with matched-control KD patients with normal EF. These findings raise concern for myocardial fibrosis as a potential late sequela of the more severe myocarditis experienced by a subset of KD patients during the acute phase

Optimal Time of Arrival Estimation for MIMO Backscatter Channels

In this paper, we propose a novel time of arrival (TOA) estimator for multiple-input-multiple-output (MIMO) backscatter channels in closed form. The proposed estimator refines the estimation precision from the topological structure of the MIMO backscatter channels, and can considerably enhance the estimation accuracy. Particularly, we show that for the general $M \times N$ bistatic topology, the mean square error (MSE) is $\frac{M+N-1}{MN}\sigma^2_0$, and for the general $M \times M$ monostatic topology, it is $\frac{2M-1}{M^2}\sigma^2_0$ for the diagonal subchannels, and $\frac{M-1}{M^2}\sigma^2_0$ for the off-diagonal subchannels, where $\sigma^2_0$ is the MSE of the conventional least square estimator. In addition, we derive the Cramer-Rao lower bound (CRLB) for MIMO backscatter TOA estimation which indicates that the proposed estimator is optimal. Simulation results verify that the proposed TOA estimator can considerably improve both estimation and positioning accuracy, especially when the MIMO scale is large