Detecting changes in the mean of functional observations

Summary.  Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as X _i ( t )= μ ( t )+Σ_{1≤ l <∞} η _{i ,  l} +  v _l ( t ), where μ is the common mean, v _l are the eigenfunctions of the covariance operator and the η _{i ,  l} are the scores. Inferential procedures assume that the mean function μ ( t ) is the same for all values of i . If, in fact, the observations do not come from one population, but rather their mean changes at some point(s), the results of principal component analysis are confounded by the change(s). It is therefore important to develop a methodology to test the assumption of a common functional mean. We develop such a test using quantities which can be readily computed in the R package fda. The null distribution of the test statistic is asymptotically pivotal with a well-known asymptotic distribution. The asymptotic test has excellent finite sample performance. Its application is illustrated on temperature data from England.     

Order preserving property of moment estimators

Balakrishnan and Mi (2001) considered order preserving property of maximum likelihood estimators. In this paper there are given conditions under which the moment estimators have the property of preserving stochastic orders. The preserving property for the usual stochastic order as well as for likelihood ratio one is considered. Sufficient conditions are established for some parametric families of distributions.     

Multiscale interpretation of taut string estimation and its connection to Unbalanced Haar wavelets

We compare two state-of-the-art non-linear techniques for nonparametric function estimation via piecewise constant approximation: the taut string and the Unbalanced Haar methods. While it is well-known that the latter is multiscale, it is not obvious that the former can also be interpreted as multiscale. We provide a unified multiscale representation for both methods, which offers an insight into the relationship between them as well as suggesting lessons both methods can learn from each other.     

Invariant dependence structure under univariate truncation: the high-dimensional case

In this paper, the class of all multivariate copulas that are invariant under univariate truncation is characterized.     

Hard Times! How do Households Cope with Financial Difficulties? Evidence from the Swiss Household Panel

This study investigates impact of debt arrears and various consequential compensatory actions on self-reported satisfaction with life and the financial situation. The link between financial difficulties and the responses they demand has rarely been translated into satisfaction measures in the past. This study informs the literature about actual consequences of problems with arrears and impact of different coping strategies on household satisfaction measures. To address the questions at hand, data from the six (2010–2015) waves of the Swiss Household Panel were examined. A panel data model with fixed effects estimator was applied to account for unobserved population heterogeneity and mitigate the issues of omitted variables. The study confirmed that severe debt problems disproportionally affected self-reported satisfaction measures. Responses to arrears, if representing likely long-term solutions, did not signify further deterioration in self-reported measures. However, if arrears required resort to bank credit, disposal of household valuables or borrowing from family and friends, satisfaction with the household financial situation and household head life satisfaction were likely to suffer more.     

Two sample inference in functional linear models

We propose a method of comparing two functional linear models in which explanatory variables are functions (curves) and responses can be either scalars or functions. In such models, the role of parameter vectors (or matrices) is played by integral operators acting on a function space. We test the null hypothesis that these operators are the same in two independent samples. The complexity of the test statistics increases as we move from scalar to functional responses and relax assumptions on the covariance structure of the regressors. They all, however, have an asymptotic chi‐squared distribution with the number of degrees of freedom which depends on a specific setting. The test statistics are readily computable using the R package fda , and have good finite sample properties. The test is applied to egg‐laying curves of Mediterranean flies and to data from terrestrial magnetic observatories. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Absolutely Continuous Copulas with Given Diagonal Sections

Necessary and sufficient conditions are given in order to ensure that a function δ:[0, 1] → [0, 1] is the diagonal section of an absolutely continuous copula. Explicit constructions are provided.     

Social welfare in the light of topic modelling

With an increased focus on social well-being in response to a burgeoning global economy exposing the weaknesses of social welfare policies, research output in the field has grown exponentially. Keeping track of the evolving research themes proves difficult due to the steady rise in the number of studies published in the interdisciplinary field of social welfare. Therefore, researchers need a comprehensive overview to confirm the current shape of the field based on the published research. Using a latent Dirichlet allocation algorithm as a topic modelling technique, this study identified 12 prominent themes from more than 10,000 research outputs on social welfare published from 2000 to 2020 in Scopus-indexed journals. Such an exploratory text-mining approach to literature review provides broad insights into the diversity of research and may serve as a foundation for further in-depth studies. Identifying these 12 thematic areas and their sub-themes allows us to articulate the complexity and diversity of social welfare issues, which go far beyond the field of well-established welfare economics or social work. The study shows that the topic of ‘social welfare’ has not only evolved over time but has significantly broadened its meaning. It can no longer be solely synonymous with institutional social security. We contend that research in this area needs to take into account a broader and more systematic range of determinants constituting the dynamic character of social welfare.