Multiscale fractality with application and statistical modeling and estimation for computer experiment of nano-particle fabrication

The first chapter proposes multifractal analysis to measure inhomogeneity of regularity of 1H-NMR spectrum using wavelet-based multifractal tools. The geometric summaries of multifractal spectrum are informative summaries, and as such employed to discriminate 1H-NMR spectra associated with different treatments. The methodology is applied to evaluate the effect of sulfur amino acids. The second part of this thesis provides essential materials for understanding engineering background of a nano-particle fabrication process. The third chapter introduces a constrained random effect model. Since there are certain combinations of process variables resulting to unproductive process outcomes, a logistic model is used to characterize such a process behavior. For the cases with productive outcomes a normal regression serves the second part of the model. Additionally, random-effects are included in both logistics and normal regression models to describe the potential spatial correlation among data. This chapter researches a way to approximate the likelihood function and to find estimates for maximizing the approximated likelihood. The last chapter presents a method to decide the sample size under multi-layer system. The multi-layer is a series of layers, which become smaller and smaller. Our focus is to decide the sample size in each layer. The sample size decision has several objectives, and the most important purpose is the sample size should be enough to give a right direction to the next layer. Specifically, the bottom layer, which is the smallest neighborhood around the optimum, should meet the tolerance requirement. Performing the hypothesis test of whether the next layer includes the optimum gives the required sample size.PhDCommittee Chair: Brani Vidakovic ; Committee Chair: Jye-Chyi (JC) Lu; Committee Co-Chair: Martha Grover; Committee Member: Jianjun Shi; Committee Member: Kamran Paynaba

The 8th International Conference on Time Series and Forecasting

The aim of ITISE 2022 is to create a friendly environment that could lead to the establishment or strengthening of scientific collaborations and exchanges among attendees. Therefore, ITISE 2022 is soliciting high-quality original research papers (including significant works-in-progress) on any aspect time series analysis and forecasting, in order to motivating the generation and use of new knowledge, computational techniques and methods on forecasting in a wide range of fields

Confidence sets for change-point problems in nonparametric regression

In this thesis, confidence sets for different nonparametric regression problems with change-points are developed. Uniform and pointwise asymptotic confidence bands for the jump-location-curve in a boundary fragment model using methods from M-estimation and Gaussian approximation are constructed for the rotated difference kernel estimator. In addition, estimation of the location and of the height of the jump in some derivative of a regression curve is considered. Optimal convergence rates as well as the joint asymptotic normal distribution of estimators based on the zero-crossing-time technique are established over certain Hölder-classes. Further, joint as well as marginal asymptotic confidence sets which are honest and adaptive for these parameters over specific Hölder-classes are constructed. The finite-sample performance is investigated in simulation studies, and real data illustrations are given

Attitudes towards old age and age of retirement across the world: findings from the future of retirement survey

The 21st century has been described as the first era in human history when the world will no longer be young and there will be drastic changes in many aspects of our lives including socio-demographics, financial and attitudes towards the old age and retirement. This talk will introduce briefly about the Global Ageing Survey (GLAS) 2004 and 2005 which is also popularly known as “The Future of Retirement”. These surveys provide us a unique data source collected in 21 countries and territories that allow researchers for better understanding the individual as well as societal changes as we age with regard to savings, retirement and healthcare. In 2004, approximately 10,000 people aged 18+ were surveyed in nine counties and one territory (Brazil, Canada, China, France, Hong Kong, India, Japan, Mexico, UK and USA). In 2005, the number was increased to twenty-one by adding Egypt, Germany, Indonesia, Malaysia, Poland, Russia, Saudi Arabia, Singapore, Sweden, Turkey and South Korea). Moreover, an additional 6320 private sector employers was surveyed in 2005, some 300 in each country with a view to elucidating the attitudes of employers to issues relating to older workers. The paper aims to examine the attitudes towards the old age and retirement across the world and will indicate some policy implications

Confidence sets for change-point problems in nonparametric regression

In this thesis, confidence sets for different nonparametric regression problems with change-points are developed. Uniform and pointwise asymptotic confidence bands for the jump-location-curve in a boundary fragment model using methods from M-estimation and Gaussian approximation are constructed for the rotated difference kernel estimator. In addition, estimation of the location and of the height of the jump in some derivative of a regression curve is considered. Optimal convergence rates as well as the joint asymptotic normal distribution of estimators based on the zero-crossing-time technique are established over certain Hölder-classes. Further, joint as well as marginal asymptotic confidence sets which are honest and adaptive for these parameters over specific Hölder-classes are constructed. The finite-sample performance is investigated in simulation studies, and real data illustrations are given

Advanced methods for analysing and modelling multivariate palaeoclimatic time series

The separation of natural and anthropogenically caused climatic changes is an important task of contemporary climate research. For this purpose, a detailed knowledge of the natural variability of the climate during warm stages is a necessary prerequisite. Beside model simulations and historical documents, this knowledge is mostly derived from analyses of so-called climatic proxy data like tree rings or sediment as well as ice cores. In order to be able to appropriately interpret such sources of palaeoclimatic information, suitable approaches of statistical modelling as well as methods of time series analysis are necessary, which are applicable to short, noisy, and non-stationary uni- and multivariate data sets. Correlations between different climatic proxy data within one or more climatological archives contain significant information about the climatic change on longer time scales. Based on an appropriate statistical decomposition of such multivariate time series, one may estimate dimensions in terms of the number of significant, linear independent components of the considered data set. In the presented work, a corresponding approach is introduced, critically discussed, and extended with respect to the analysis of palaeoclimatic time series. Temporal variations of the resulting measures allow to derive information about climatic changes ...thesi

Distance-based analysis of dynamical systems and time series by optimal transport

The concept of distance is a fundamental notion that forms a basis for the orientation in space. It is related to the scientific measurement process: quantitative measurements result in numerical values, and these can be immediately translated into distances. Vice versa, a set of mutual distances defines an abstract Euclidean space. Each system is thereby represented as a point, whose Euclidean distances approximate the original distances as close as possible. If the original distance measures interesting properties, these can be found back as interesting patterns in this space. This idea is applied to complex systems: The act of breathing, the structure and activity of the brain, and dynamical systems and time series in general. In all these situations, optimal transportation distances are used; these measure how much work is needed to transform one probability distribution into another. The reconstructed Euclidean space then permits to apply multivariate statistical methods. In particular, canonical discriminant analysis makes it possible to distinguish between distinct classes of systems, e.g., between healthy and diseased lungs. This offers new diagnostic perspectives in the assessment of lung and brain diseases, and also offers a new approach to numerical bifurcation analysis and to quantify synchronization in dynamical systems.LEI Universiteit LeidenNWO Computational Life Sciences, grant no. 635.100.006Analyse en stochastie

Flood Forecasting Using Machine Learning Methods

This book is a printed edition of the Special Issue Flood Forecasting Using Machine Learning Methods that was published in Wate