A test of significance in functional quadratic regression

We consider a quadratic functional regression model in which a scalar response depends on a functional predictor; the common functional linear model is a special case. We wish to test the significance of the nonlinear term in the model. We develop a testing method which is based on projecting the observations onto a suitably chosen finite dimensional space using functional principal component analysis. The asymptotic behavior of our testing procedure is established. A simulation study shows that the testing procedure has good size and power with finite sample sizes. We then apply our test to a data set provided by Tecator, which consists of near-infrared absorbance spectra and fat content of meat.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ446 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Detecting changes in functional linear models

We observe two sequences of curve which are connected via an integral operator. Our model includes linear models as well as autoregressive models in Hilbert spaces. We wish to test the null hypothesis that the operator did not change during the observation period. Our method is based on projecting the observations onto a suitably chosen finite dimensional space. The testing procedure is based on functionals of the weighted residuals of the projections. Since the quadratic form is based on estimating the long-term covariance matrix of the residuals, we also provide some results on Bartlett-type estimators

Doctor of Philosophy

dissertationThis dissertation is concerned with functional data analysis. Functional data consists of a collection of curves or functions defi ned on an interval. These curves can be obtained by splitting a continuous time record such as temperature into daily or annual curves. Functional data is also obtained when an experimenter records a curve of data from each subject in a sample, e.g., a growth trajectory of an animal or plant. Several examples of diff erent models for functional data are given. We use the method of principle component analysis to obtain the necessary regularization in each model. Functional principal component analysis is summarized as a natural extension of the traditional vector principal component analysis. The first functional model is concerned with inference based on the mean function of a functional time series. We develop and asymptotically justify a testing procedure for the equality of means in two functional samples exhibiting temporal dependence. As a second example, we consider a quadratic functional regression model in which a scalar response depends on a functional predictor. We develop a test of the significance of the nonlinear term in the model. The asymptotic behavior of our testing procedure is established. In the third model, we observe two sequences of curves which are connected via an integral operator. This model includes linear models as well as autoregressive models in Hilbert spaces. We develop a procedure to test the stability of the model. In the fourth model, we propose a functional version of the popular ARCH model. We establish conditions for the existence of a strictly stationary solution, derive weak dependence and moment conditions, show consistency of the estimators, and perform an empirical study demonstrating how our model matches with real data

Severe Acute Kidney Injury is Associated with Increased Risk of Death and New Morbidity After Pediatric Septic Shock

Objectives: Acute kidney injury is common in critically ill children; however, the frequency of septic shock-associated acute kidney injury and impact on functional status are unknown. We evaluated functional outcomes of children with septic shock-associated acute kidney injury. Design: Secondary analysis of patients with septic shock from the prospective Life after Pediatric Sepsis Evaluation study. We defined acute kidney injury using Kidney Disease Improving Global Outcomes criteria, comparing patients with absent/Stage 1 acute kidney injury to those with Stage 2/3 acute kidney injury (severe acute kidney injury). Our primary outcome was a composite of mortality or new functional morbidity at day 28 of hospitalization or discharge. We also assessed poor long-term outcome, defined as mortality or a persistent, serious deterioration in health-related quality of life at 3 months. Setting: Twelve academic PICUs in the United States. Patients: Critically ill children, 1 month to 18 years, with community-acquired septic shock requiring vasoactive-inotropic support. Interventions: None. Measurements and main results: More than 50% of patients (176/348) developed severe acute kidney injury; of those, 21.6% (38/176) required renal replacement therapy. Twice as many patients with severe acute kidney injury died or developed new substantive functional morbidity (38.6 vs 16.3%; p < 0.001). After adjustment for age, malignancy, and initial illness severity, severe acute kidney injury was independently associated with mortality or new substantive morbidity (adjusted odds ratio, 2.78; 95% CI, 1.63-4.81; p < 0.001). Children with severe acute kidney injury had poorer health-related quality of life at 3 months (adjusted effect size 2.46; 95% CI, 1.44-4.20; p = 0.002). Children with severe acute kidney injury required longer duration of mechanical ventilation (11.0 vs 7.0 d; p < 0.001) and PICU stay (11.7 vs 7.1 d; p < 0.001). Conclusions: Among children with septic shock, severe acute kidney injury was independently associated with increased risk of death or new substantive functional morbidity. Survivors of sepsis with severe acute kidney injury were more likely to have persistent, serious health-related quality of life deterioration at 3 months

Measurement of (anti)deuteron and (anti)proton production in DIS at HERA

The first observation of (anti)deuterons in deep inelastic scattering at HERA has been made with the ZEUS detector at a centre-of-mass energy of 300--318 GeV using an integrated luminosity of 120 pb-1. The measurement was performed in the central rapidity region for transverse momentum per unit of mass in the range 0.3<p_T/M<0.7. The particle rates have been extracted and interpreted in terms of the coalescence model. The (anti)deuteron production yield is smaller than the (anti)proton yield by approximately three orders of magnitude, consistent with the world measurements.Comment: 26 pages, 9 figures, 5 tables, submitted to Nucl. Phys.

High-E_T dijet photoproduction at HERA

The cross section for high-E_T dijet production in photoproduction has been measured with the ZEUS detector at HERA using an integrated luminosity of 81.8 pb-1. The events were required to have a virtuality of the incoming photon, Q^2, of less than 1 GeV^2 and a photon-proton centre-of-mass energy in the range 142 < W < 293 GeV. Events were selected if at least two jets satisfied the transverse-energy requirements of E_T(jet1) > 20 GeV and E_T(jet2) > 15 GeV and pseudorapidity requirements of -1 < eta(jet1,2) < 3, with at least one of the jets satisfying -1 < eta(jet) < 2.5. The measurements show sensitivity to the parton distributions in the photon and proton and effects beyond next-to-leading order in QCD. Hence these data can be used to constrain further the parton densities in the proton and photon.Comment: 36 pages, 13 figures, 20 tables, including minor revisions from referees. Accepted by Phys. Rev.