Quadratic perturbation expansions of certain functions of eigenvalues and eigenvectors and their application to sensitivity analysis in multivariate methods

Tanaka (1988) lias derived the influence functions, which are equivalent to the perturbation expansions up to linear terms, of two functions of eigenvalues and eigenvectors of a real symmetric matrix, and applied them to principal component analysis. The present paper deals with the perturbation expansions up to quadratic terms of the same functions and discusses their application to sensitivity analysis in multivariate methods, in particular, principal component analysis and principal factor analysis. Numerical examples are given to show how the approximation improves with the quadratic terms.     

Nonparametric product partition models for multiple change-points analysis

ABSTRACT

We propose an extension of parametric product partition models. We name our proposal nonparametric product partition models because we associate a random measure instead of a parametric kernel to each set within a random partition. Our methodology does not impose any specific form on the marginal distribution of the observations, allowing us to detect shifts of behaviour even when dealing with heavy-tailed or skewed distributions. We propose a suitable loss function and find the partition of the data having minimum expected loss. We then apply our nonparametric procedure to multiple change-point analysis and compare it with PPMs and with other methodologies that have recently appeared in the literature. Also, in the context of missing data, we exploit the product partition structure in order to estimate the distribution function of each missing value, allowing us to detect change points using the loss function mentioned above. Finally, we present applications to financial as well as genetic data.     

Strong consistency of presmoothed Kaplan–Meier integrals when covariables are present

It is known that the Kaplan–Meier estimation may be improved via presmoothing methods. In this article, we introduce an extended presmoothed Kaplan–Meier estimator in the presence of covariates. The main result is the strong consistency of general empirical integrals based on such an estimator. As applications, one can obtain a consis-tent multivariate empirical distribution under censoring, and also can obtain a consistent estimation of regression parameters. We illustrate the new estimation methods through simulations and real data analysis.     

On time-irreversibility and other non-linear features in time series

Time-irreversibility, asymmetry of the distribution, and the occurrence of sudden bursts are considered, amongst others, as non-linear features in time series modeling. The implication is often made that time series showing these features must be analyzed using non-linear models. In contrast, this paper shows that time-irreversible asymmetric time series showing certain types of sudden bursts may be generated by linear models with adequate input sequences. Thus some non-linear time series features may be caused by the pattern in the input sequence rather than by non-linearity in the model. Examples are considered to illustrate the situation.     

Random translation of discrete order statistics

We investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose order statistics are related by a random translation. We also provide some examples using the constructive method that we propose.     

On the recoding of continuous and bounded indexes to a binomial form: an application to quality-of-life scores

The statistical analysis of patient-reported outcomes (PROs) as endpoints has shown to be of great practical relevance. The resulting scores or indexes from the questionnaires used to measure PROs could be treated as continuous or ordinal. The goal of this study is to propose and evaluate a recoding process of the scores, so that they can be treated as binomial outcomes and, therefore, analyzed using logistic regression with random effects. The general methodology of recoding is based on the observable values of the scores. In order to obtain an optimal recoding, the evaluation of the recoding method is tested for different values of the parameters of the binomial distribution and different probability distributions of the random effects. We illustrate, evaluate and validate the proposed method of recoding with the Short Form-36 (SF-36) Survey and real data. The optimal recoding approach is very useful and flexible. Moreover, it has a natural interpretation, not only for ordinal scores, but also for questionnaires with many dimensions and different profiles, where a common method of analysis is desired, such as the SF-36.     

Bayesian influence diagnostics in radiocarbon dating

Linear models constitute the primary statistical technique for any experimental science. A major topic in this area is the detection of influential subsets of data, that is, of observations that are influential in terms of their effect on the estimation of parameters in linear regression or of the total population parameters. Numerous studies exist on radiocarbon dating which propose a value consensus and remove possible outliers after the corresponding testing. An influence analysis for the value consensus from a Bayesian perspective is developed in this article.     

Migration and the senses

Recent scholarship in the sociological subfields of culture and immigration offers several promising directions for studying how people experience the world in embodied ways and move through and across boundaries. Yet, the lack of overlap between fields has left numerous theoretical angles unexplored. In this review, I consider the limited existing scholarship at the intersection of migration and the senses. I discuss literature on the role of sensation during three critical moments of migration: movement, encounter, and return. These moments highlight the sensorially dislocating nature of travel, the felt politics of inclusion and exclusion, and the transporting power of embodied memories. These works dive deep into the everyday realities of bodies on the move that public and academic discourse has previously ignored. I conclude by briefly outlining exciting new directions to expand work connecting migration and the senses and suggest that we begin to explore globalized migrant sensibilities.     

ISO 45001 and controversial transnational private regulation for occupational health and safety

This article analyses the genesis of the ISO 45001 standard on occupational health and safety, a new initiative of transnational private regulation. The authors draw a picture of controversy from interviews with stakeholders involved in its design, approval and initial dissemination, and from a qualitative content analysis of the internal documentation of the committee responsible for its approval. Like its predecessors relating to environmental management – ISO 14001 – and corporate social responsibility – ISO 26000 – this new standard raises serious concerns among stakeholders given that it deals with substantive political, social and legal issues.     

Ethnic–Racial Socialization in the Family: A Decade's Advance on Precursors and Outcomes

In the current decade, the U.S. population reached historically high levels of ethnic–racial diversity and reelected the nation's first Black–White biracial President. Simultaneously, scholars also documented significant ethnic–racial inequities in education, increased xenophobia, and a racial climate that revealed deep-seated ethnic–racial tensions. Given this backdrop and acknowledging the significant role that families play in youths' abilities to navigate their social contexts, the current review focused on the literature on families' ethnic–racial socialization efforts with youth from the 2010 decade. Our review of 259 empirical articles revealed that there has been an exponential increase in research on family ethnic–racial socialization in this decade. Furthermore, although it is clear that family ethnic–racial socialization is a robust predictor of youths' adjustment, the associations between socialization and adjustment must be considered with attention to specific socialization strategies, the confluence of strategies used, and the unique contexts within which families' lives are embedded.