On the Number of Independent Pieces of Information in a Functional Linear Model with a Scalar Response

In a functional linear model (FLM) with scalar response, the parameter curve quantifies the relationship between a functional explanatory variable and a scalar response. While these models can be ill-posed, a penalized regression spline approach may be used to obtain an estimate of the parameter curve. The penalized regression spline estimate will be dependent on the value of a smoothing parameter. However, the ability to obtain a reasonable parameter curve estimate is reliant on how much information is present in the covariate functions for estimating the parameter curve. We propose to quantify the information present in the covariate functions to estimate the parameter curve. In addition, we examine the influence of this information on the stability of the parameter curve estimator and on the performance of smoothing parameter selection methods in a FLM with a scalar response.

CDBTools - Evaluate Positron Annihilation Coincidence Doppler Broadening Spectrum

CDBTools is a lightweight and easy to use application designed to provide you with an analysis tool for coincidence Doppler broadening (CDB) of the positron annihilation energy spectrum files. This application enables you to analyze the CDB and ratio curves, plots as well as graphs representing the evolution of the orbital electron momentum spectrum. The CDB extraction is provided by selectable filters applied at the diagonal line of the input matrix. To achieve CDB ratio curves with minimal error caused by 511keV peak shift, spectrum curves are recalculated by penalized regression spline.

Serum 25-hydroxyvitamin D and the risk of stroke in Hong Kong Chinese

SummaryLow vitamin D levels have been associated with various cardiovascular diseases; however, whether it is associated with stroke remains inconclusive. We aimed to evaluate the association between serum 25-hydroxyvitamin D and risk of stroke. We conducted a cohort study consisting of 3,458 participants from the Hong Kong Osteoporosis Study aged ≥45 at baseline, examined between 1995 and 2010 and followed up using electronic medical records. Ischaemic and haemorrhagic stroke were defined using the ICD-9 code. In multivariable Cox-proportional hazard regression, quintiles 1 and 4 were significantly associated with increased risk of stroke when compared to the highest quintile (Quintile 1: HR, 1.78; 95 % CI, 1.16–2.74 and quintile 4: HR, 1.61; 95 % CI, 1.07–2.43). A similar association was observed in both men and women. In subgroup analysis, the association was specifically observed for ischaemic stroke, but not haemorrhagic stroke. Using a penalized regression spline, the association between vitamin D and risk of stroke was in a reverse J-shape, with the lowest risk of stroke being observed at 25(OH)D levels between 70 and 80 nmol/l. In conclusion, a low vitamin D level is associated with increased risk of ischaemic stroke; however, whether high vitamin D level is also associated with increased risk of stroke requires further study.Supplementary Material to this article is available at www.thrombosis-online.com.

ON THE INTERACTION BETWEEN ECONOMIC GROWTH AND BUSINESS CYCLES

The present paper studies the interaction between short-run business cycle fluctuations and economic growth at the empirical level. We identify a measure of potential output with that rate of growth consistent with a constant unemployment rate, and we estimate the effects of GDP growth rates on the latter in 13 Latin American and 18 OECD countries during the period 1981–2011. The results of both parametric (OLS/IV and a panel estimator that allows for parameter heterogeneity and cross-section dependence) and nonparametric (a penalized regression spline estimator) econometric techniques show that the measure of potential output experiences positive (negative) changes in periods of high (low) growth in the majority of countries. However, in contrast to the sample of OECD countries, we find that less than half of the sample of Latin American countries experience statistically significant changes in this measure of potential output in periods of low growth.

Comparative Analysis for Robust Penalized Spline Smoothing Methods

Smoothing noisy data is commonly encountered in engineering domain, and currently robust penalized regression spline models are perceived to be the most promising methods for coping with this issue, due to their flexibilities in capturing the nonlinear trends in the data and effectively alleviating the disturbance from the outliers. Against such a background, this paper conducts a thoroughly comparative analysis of two popular robust smoothing techniques, theM-type estimator andS-estimation for penalized regression splines, both of which are reelaborated starting from their origins, with their derivation process reformulated and the corresponding algorithms reorganized under a unified framework. Performances of these two estimators are thoroughly evaluated from the aspects of fitting accuracy, robustness, and execution time upon the MATLAB platform. Elaborately comparative experiments demonstrate that robust penalized spline smoothing methods possess the capability of resistance to the noise effect compared with the nonrobust penalized LS spline regression method. Furthermore, theM-estimator exerts stable performance only for the observations with moderate perturbation error, whereas theS-estimator behaves fairly well even for heavily contaminated observations, but consuming more execution time. These findings can be served as guidance to the selection of appropriate approach for smoothing the noisy data.

Average seasonal changes in chlorophyll a in Icelandic waters

Guðmundsson, K., Heath, M. R., and Clarke, E. D. 2009. Average seasonal changes in chlorophyll a in Icelandic waters. – ICES Journal of Marine Science, 66: 2133–2140. The standard algorithms used to derive sea surface chlorophyll a concentration from remotely sensed ocean colour data are based almost entirely on the measurements of surface water samples collected in open sea (case 1) waters which cover ∼60% of the worlds oceans, where strong correlations between reflectance and chlorophyll concentration have been found. However, satellite chlorophyll data for waters outside the defined case 1 areas, but derived using standard calibrations, are frequently used without reference to local in situ measurements and despite well-known factors likely to lead to inaccuracy. In Icelandic waters, multiannual averages of 8-d composites of SeaWiFS chlorophyll concentration accounted for just 20% of the variance in a multiannual dataset of in situ chlorophyll a measurements. Nevertheless, applying penalized regression spline methodology to model the spatial and temporal patterns of in situ measurements, using satellite chlorophyll as one of the predictor variables, improved the correlation considerably. Day number, representing seasonal variation, accounted for substantial deviation between SeaWiFS and in situ estimates of surface chlorophyll. The final model, using bottom depth and bearing to the sampling location as well as the two variables mentioned above, explained 49% of the variance in the fitting dataset.