The Mellin transform in Nonparametric Statistics

This thesis deals with the nonparametric estimation for a special class of ill-posed inverse prob- lems, the so-called multiplicative measurement error models. In these models, the observations of the unknown, to be estimated quantity is only accessible with a multiplicative measurement error. As a consequence, the instability of the reconstruction depends on the distribution of the error by effecting the ill-posedness of the underlying inverse problem. The theory of Mellin transform al- lows to express the influence of the error distribution on the instability of the reconstruction and to reduce the estimation of the unknown quantity to a regularized estimation of its unknown Mellin transform. The proposed estimation strategies will be evaluated in terms of a mean weighted(- integrated) squared risk. Aside from being an introduction to the theory of Mellin transforms and multiplicative convolu- tions, this thesis is structuered in three topics. In the first part, we consider global density estimation under multiplicative measurement error. After a comparison between direct and noisy observations, we study several families of error dis- tributions, the multivariate case and the influence of dependence structures in the data. Here in each case we will propose an estimation strategy, discuss its minimax-optimality and consider data- driven choices of smoothing parameters. The theoritcal expected behavior of the estimators are illustrated through Monte-Carlo simulations. In the second part, we study global survival function estimation, which is, alongside the density of a distribution, a frequently considered characterization of a distribution. We once again propose an estimation method, prove its minimax-optimality and discuss data-driven choices of smoothing parameters. Furthermore, we analyse the stability of the estimator for Bernoulli-shift processes and visualize it using a Monte-Carlo simulation. The third part considers the estimation of the evaluation of an linear functional under multiplicative measurement errors. The point evaluation of the density, the survival function and the cumulative distribution function, to mention only a few, can be intrepreted as an evaluation of a linear func- tional. This allows the simultaneous analysis of these different estimation problems and the com- parison of the ill-posedness of the underlying inverse problems. A minimax-optimal estimation strategy as well as a data-driven choice of the smoothing parameters are presented and analyzed

Adaptive local density estimation in tomography

We study the non-parametric estimation of a multidimensional unknown density f in a tomography problem based on independent and identically distributed observations, whose common density is proportional to the Radon transform of f. We identify the underlying statistical inverse problem and use a spectral cut-off regularisation to deduce an estimator. A fully data-driven choice of the cut-off parameter m in R+ is proposed and studied. To discuss the bias-variance trade off, we consider Sobolev spaces and show the minimax-optimality of the spectral cut-off density estimator. In a simulation study, we illustrate a reasonable behaviour of the studied fully data-driven estimator.Comment: 19 pages, 8 figure

Multiplicative deconvolution under unknown error distribution

We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y = X\cdot U$ of $X$. The multiplicative measurement error $U$ is supposed to be independent of $X$. The objective of this work is to construct a fully data-driven estimation procedure when the error density $f^U$ is unknown. We assume that in addition to the i.i.d. sample from $Y$, we have at our disposal an additional i.i.d. sample drawn independently from the error distribution. The proposed estimation procedure combines the estimation of the Mellin transformation of the density $f$ and a regularisation of the inverse of the Mellin transform by a spectral cut-off. The derived risk bounds and oracle-type inequalities cover both - the estimation of the density $f$ as well as the survival function $S^X$. The main issue addressed in this work is the data-driven choice of the cut-off parameter using a model selection approach. We discuss conditions under which the fully data-driven estimator can attain the oracle-risk up to a constant without any previous knowledge of the error distribution. We compute convergences rates under classical smoothness assumptions. We illustrate the estimation strategy by a simulation study with different choices of distributions

Elevated high sensitive C-reactive protein in fibromyalgia

IntroductionFibromyalgia syndrome (FMS) is a complex chronic pain condition characterized by widespread pain and tenderness, fatigue, and sleep disturbances. Currently, factors contributing to FMS are considered to be multifactorial, and the involvement of inflammatory processes is a question of debate.ObjectiveThe aims of this study were (1) to assess whether serum concentrations of high-sensitivity C-reactive protein (hsCRP) differ between individuals diagnosed with FMS and pain-free controls, (2) to determine whether these differences are associated with clinical symptoms, and (3) to explore whether the observed differences can be explained by specific covariates such as age, weight, and smoking status.MethodsAn ANOVA was applied to identify differences of hsCRP levels between FMS and pain-free controls and an analysis of covariance (ANCOVA) was performed to investigate the dependencies of hsCRP with respect to covariates. To assess the reliability of our findings, we also utilized a Bayesian robust estimation model to determine the level of confidence associated with our results.ResultsThe results showed that individuals with FMS had higher hsCRP levels compared to healthy controls [F(1,106) = 8.802, p < 0.001] and that higher hsCRP levels were significant correlated with a higher symptom burden (r = 0. 287, p = 0.008) and more tender points (r = 0.307, p = 0.005). Further, hsCRP levels were significantly associated with weight (η2 = 0.154, p < 0.001), but independent of age (η2 = 0.005, p = 0.42), smoking status (η2 = 0.002, p = 0.623), or gender (η2 = 0.0045, p = 0.437), which resulted in an insignificant group effect between FMS and controls (η2 = 0.029, p = 0.052), even after controlling for covariates.ConclusionIn conclusion, this study provides evidence that sub-inflammatory processes correlate with clinical symptoms, which can be partly attributed to differences in weight, but cannot be fully explained by them. Further research is needed to elucidate the mechanisms underlying the association between hsCRP and FMS and to explore the potential therapeutic implications of targeting hsCRP in the management of FMS

Lo glocal y el turismo. Nuevos paradigmas de interpretación.

El estudio del turismo se realiza desde múltiples escalas y enfoques, este libro aborda muchos temas que es necesario discutir desde diversas perspectivas; es el caso de la reflexión sobre la propia disciplina y sus conceptos, así como los asuntos específicos referidos al impacto territorial, los tipos de turismo, las cuestiones ambientales, el tema de la pobreza, la competitividad, las políticas públicas, el papel de las universidades, las áreas naturales protegidas, la sustentabilidad, la cultura, el desarrollo, la seguridad, todos temas centrales documentados y expuestos con originalidad y dominio del asunto. Lo multiescalar es básico para la comprensión del sistema turístico, sistema formado de procesos globales, regionales y locales. El eje de discusión del libro es lo glocal, esa interacción entre lo nacional y local con lo global

Use of multidimensional item response theory methods for dementia prevalence prediction : an example using the Health and Retirement Survey and the Aging, Demographics, and Memory Study

Background Data sparsity is a major limitation to estimating national and global dementia burden. Surveys with full diagnostic evaluations of dementia prevalence are prohibitively resource-intensive in many settings. However, validation samples from nationally representative surveys allow for the development of algorithms for the prediction of dementia prevalence nationally. Methods Using cognitive testing data and data on functional limitations from Wave A (2001-2003) of the ADAMS study (n = 744) and the 2000 wave of the HRS study (n = 6358) we estimated a two-dimensional item response theory model to calculate cognition and function scores for all individuals over 70. Based on diagnostic information from the formal clinical adjudication in ADAMS, we fit a logistic regression model for the classification of dementia status using cognition and function scores and applied this algorithm to the full HRS sample to calculate dementia prevalence by age and sex. Results Our algorithm had a cross-validated predictive accuracy of 88% (86-90), and an area under the curve of 0.97 (0.97-0.98) in ADAMS. Prevalence was higher in females than males and increased over age, with a prevalence of 4% (3-4) in individuals 70-79, 11% (9-12) in individuals 80-89 years old, and 28% (22-35) in those 90 and older. Conclusions Our model had similar or better accuracy as compared to previously reviewed algorithms for the prediction of dementia prevalence in HRS, while utilizing more flexible methods. These methods could be more easily generalized and utilized to estimate dementia prevalence in other national surveys

ECMO for COVID-19 patients in Europe and Israel

Since March 15th, 2020, 177 centres from Europe and Israel have joined the study, routinely reporting on the ECMO support they provide to COVID-19 patients. The mean annual number of cases treated with ECMO in the participating centres before the pandemic (2019) was 55. The number of COVID-19 patients has increased rapidly each week reaching 1531 treated patients as of September 14th. The greatest number of cases has been reported from France (n = 385), UK (n = 193), Germany (n = 176), Spain (n = 166), and Italy (n = 136) .The mean age of treated patients was 52.6 years (range 16–80), 79% were male. The ECMO configuration used was VV in 91% of cases, VA in 5% and other in 4%. The mean PaO2 before ECMO implantation was 65 mmHg. The mean duration of ECMO support thus far has been 18 days and the mean ICU length of stay of these patients was 33 days. As of the 14th September, overall 841 patients have been weaned from ECMO support, 601 died during ECMO support, 71 died after withdrawal of ECMO, 79 are still receiving ECMO support and for 10 patients status n.a. . Our preliminary data suggest that patients placed on ECMO with severe refractory respiratory or cardiac failure secondary to COVID-19 have a reasonable (55%) chance of survival. Further extensive data analysis is expected to provide invaluable information on the demographics, severity of illness, indications and different ECMO management strategies in these patients