Changes in atmospheric radiation from the statistical point of view

Modelling of changes in atmospheric radiation within the last decade is considered. First, vertical atmospheric radiation profiles are considered as a sample of functional variables and the dependence on time is estimated by a non-parametric regression (kernel smoothing). As a main result, parametric functional multiplicative regression models are provided. In particular, non-periodic models are motivated in a straightforward way by the observed data, while periodic proposals respect a hypothetical relation between atmospheric radiation and the 11-years solar cycle. Finally, some remarks on computational aspects and the choice of a suitable function space are given.

[1]  Ricardo Fraiman,et al.  An anova test for functional data , 2004, Comput. Stat. Data Anal..

[2]  P. Vieu,et al.  Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics) , 2006 .

[3]  K. J. Utikal,et al.  Inference for Density Families Using Functional Principal Component Analysis , 2001 .

[4]  Henry W. Altland,et al.  Applied Functional Data Analysis , 2003, Technometrics.

[5]  Pascal Sarda,et al.  No effect and lack-of-fit permutation tests for functional regression , 2007, Comput. Stat..

[6]  André Mas,et al.  Testing hypotheses in the functional linear model , 2003 .

[7]  Jane-Ling Wang,et al.  A FUNCTIONAL MULTIPLICATIVE EFFECTS MODEL FOR LONGITUDINAL DATA, WITH APPLICATION TO REPRODUCTIVE HISTORIES OF FEMALE MEDFLIES. , 2003, Statistica Sinica.

[8]  J. Ramsay,et al.  Some Tools for Functional Data Analysis , 1991 .

[9]  Frédéric Ferraty,et al.  The Functional Nonparametric Model and Application to Spectrometric Data , 2002, Comput. Stat..

[10]  P. Vieu.  Nonparametric Regression: Optimal Local Bandwidth Choice , 1991 .

[11]  André Mas,et al.  Testing for the Mean of Random Curves: A Penalization Approach , 2007 .

[12]  J. Ramsay,et al.  Principal components analysis of sampled functions , 1986 .

[13]  James O. Ramsay,et al.  Functional Data Analysis , 2005 .

[14]  P. Sarda,et al.  Functional linear model , 1999 .

[15]  Jane-ling Wang,et al.  Functional linear regression analysis for longitudinal data , 2005, math/0603132.

[16]  D. Bosq.  Linear Processes in Function Spaces: Theory And Applications , 2000 .

[17]  J. Dauxois,et al.  Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference , 1982 .