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Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions proposed so far is enjoying the combination of distribution-freeness and efficiency that makes rank-based inference a successful tool in the univariate setting. A concept of center- outward multivariate ranks and signs based on measure transportation ideas has been introduced recently. Center-outward ranks and signs are not only distribution-free but achieve in dimension d > 1 the (essential) maximal ancillarity property of traditional univariate ranks. In the present case, we show that fully distribution-free testing procedures based on center-outward ranks can achieve parametric efficiency. We establish the Hajek representation and asymptotic normality results required in the construction of such tests in multiple-output regression and MANOVA models. Simulations and an empirical study demonstrate the excellent performance of the proposed procedures., info:eu-repo/semantics/published

We propose a new nonparametric procedure to solve the problem of classifying objects represented by $d$-dimensional vectors into $K \geq 2$ groups. The newly proposed classifier was inspired by the $k$ nearest neighbour (kNN) method. It is based on the idea of a depth-based distributional neighbourhood and is called $k$ nearest depth neighbours (kNDN) classifier. The kNDN classifier has several desirable properties: in contrast to the classical kNN, it can utilize global properties of the considered distributions (symmetry). In contrast to the maximal depth classifier and related classifiers, it does not have problems with classification when the considered distributions differ in dispersion or have unequal priors. The kNDN classifier is compared to several depth-based classifiers as well as the classical kNN method in a simulation study. According to the average misclassification rates, it is comparable to the best current depth-based classifiers.

Functional two-sample tests based on empirical characteristic functionals are studied. We consider a test statistic of Cramer–von Mises type with integration over a preselected family of probability measures, say Q , leading to a computationally feasible and powerful test statistic. Small sample properties of the resulting two- and k -sample functional tests are investigated in a simulation study. In particular, we compare the resulting tests to previously proposed tests of equality of mean functions and covariance operators and we show that a proper choice of the probability measure Q gives very good power in detecting shift and scale alternatives.

Two-sample tests for functional data based on empirical characteristic functionals are proposed. The test statistic is of Cramer–von Mises type with integration over a preselected family of probability measures, say Q, leading a computationaly feasible and powerful test statistic. The choice of the probability measure Q is discussed and the empirical size and power of the resulting two-sample functional tests are investigated in a small simulation study.

© 2017 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. A major drawback of many established depth functionals is their ineffectiveness in identifying functions outlying merely in shape. Herein, a simple modification of functional depth is proposed to provide a remedy for this difficulty. The modification is versatile, widely applicable, and introduced without imposing any assumptions on the data, such as differentiability. It is shown that many favorable attributes of the original depths for functions, including consistency properties, remain preserved for the modified depths. The powerfulness of the new approach is demonstrated on a number of examples for which the known depths fail to identify the outlying functions. Supplementary material for this article is available online. ispartof: Journal of Computational and Graphical Statistics vol:26 issue:4 pages:883-893 status: published

The health care costs have been rapidly rising in recent years and the public health insurance companies are highly interested in prescription policies of general practitioners. In our contribution, a complex model for prescription behaviour of Belgian general practitioners is built using the structural equation modelling (SEM) framework. The model involves a large number of prescribed medicament groups as well as doctors’ and patients’ characteristics. As one of the results, a relatively small number of medicament groups, which effectively describe the prescription behaviour of a given doctor, is obtained. These indicators are consequently used in a generalized linear model for predicting the drug expenses per patient. Such a model can be used as a useful guideline for the expenses’ assessment of a particular practitioner.

Statistical depth functions are well-known nonparametric tools for analysing multivariate data. Halfspace depth is most frequently used, and while it has many desirable properties, it is dependent on global characteristics of the underlying distribution. In some circumstances, however, it may be desirable to take into account more local and intrinsic characteristics of the data. To this end, we introduce weighted halfspace depths in which the indicator function of closed halfspace is replaced by a more general weight function. Our approach, which calls in part on functions associated with conic sections, encompasses as special cases the notions of sample halfspace depth and kernel density estimation. We give several illustrations and prove the strong uniform consistency of weighted halfspace depth incorporating mild conditions on the weight function.

© 2015, Springer-Verlag Berlin Heidelberg. This paper concerns depth functions suitable for smooth functional data. We suggest a modification of the integrated data depth that takes into account the shape properties of the functions. This is achieved by including a derivative(s) into the definition of the suggested depth measures. We then further investigate the use of integrated data depths in supervised classification problems. The performances of classification rules based on different data depths are investigated, both in simulated and real data sets. As the proposed depth function provides a natural alternative to the depth function based on random projections, the difference in the performances of these two methods are discussed in more detail. ispartof: Computational Statistics vol:30 issue:4 pages:1011-1031 status: published

Inspired by nonlinear quantile regression, the article introduces, investigates, discusses, and illustrates a new concept of generalized elliptical location quantiles. They may require less stringent moment assumptions, be less sensitive to outliers, be less rigid, employ more a priori information regarding the location of the distribution, and have higher potential for various regression generalizations than their common elliptical predecessor defined in the convex optimization framework by means of standard linear quantile regression. Furthermore, they still include an equivalent of their predecessor as a special case and inherit most of its favorable features such as the probability interpretation, natural equivariance properties, and good behavior for elliptical and symmetric distributions, which is demonstrated both by theoretical results and data examples with convincing graphical output. On the other hand, the new elliptical quantiles need not always be uniquely defined and they require somewhat different approach to their analysis and computation due to their intrinsically non-convex formulation.

© 2016 EDP Sciences, SMAI. Several depths suitable for infinite-dimensional functional data that are available in the literature are of the form of an integral of a finite-dimensional depth function. These functionals are characterized by projecting functions into low-dimensional spaces, taking finite-dimensional depths of the projected quantities, and finally integrating these projected marginal depths over a preset collection of projections. In this paper, a general class of integrated depths for functions is considered. Several depths for functional data proposed in the literature during the last decades are members of this general class. A comprehensive study of its most important theoretical properties, including measurability and consistency, is given. It is shown that many, but not all, properties of the integrated depth are shared with the finite-dimensional depth that constitutes its building block. Some pending measurability issues connected with all integrated depth functionals are resolved, a broad new notion of symmetry for functional data is proposed, and difficulties with respect to consistency results are identified. A general universal consistency result for the sample depth version, and for the generalized median, for integrated depth for functions is derived. ispartof: ESAIM-Probability and Statistics vol:20 pages:95-130 status: published

© 2015 Elsevier Inc. A general result on weak convergence of the empirical measure of discretely observed functional data is shown. It is applied to the problem of estimation of functional mean value, and the problem of consistency of various types of depth for functional data. Counterexamples illustrating the fact that the assumptions as stated cannot be dropped easily are given. publisher: Elsevier articletitle: Weak convergence of discretely observed functional data with applications journaltitle: Journal of Multivariate Analysis articlelink: http://dx.doi.org/10.1016/j.jmva.2015.06.006 content_type: article copyright: Copyright © 2015 Elsevier Inc. All rights reserved. ispartof: Journal of Multivariate Analysis vol:146 pages:46-62 status: published

The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.

The extremal shape factor of spheroidal particles is studied in the stereological context using the extreme value theory. The domain of attraction is invariant with respect to the transformation between spatial characteristics and planar sections characteristics. It is shown that for the Farlie-Gumbel-Morgenstern bivariate distribution of size and shape factor one can estimate the normalizing constants of shape factor conditioned by unknown particle size. The theoretical solution is followed by a detailed simulation study which demonstrates the use of estimation techniques developed. The method is useful for engineering applications in materials science, where microstructural extremes correlate with the properties of materials.

In the stereological unfolding problem of size and shape factor of spheroidal particles the extremal shape factor is investigated. The transformation of particle parameters is shown to be stable with respect to the domain of attraction in three situations: (a) Conditional distribution of shape factor given particle size. (b) Conditional distribution of shape factor given particle section size. (c) Marginal distribution of shape factor. In situation (a) the normalizing constants are derived in a parametric model, which enables prediction of extreme shape factor after a preliminary solution of the size unfolding problem. In both situations (b) and (c) obtaining a similar procedure is still an open problem. The uniformity conditions necessary for (b) and (c) are shown to be mild.

This paper shows how to model seroprevalence data using change-point fractional polynomials (FPs). The inclusion of a change point in the FP framework allows to detect distortions arising from common (often untestable) assumptions made in the estimation of the age-specific prevalence and force of infection from cross-sectional data. The method is motivated using seroprevalence data on the parvovirus B19 and the varicella zoster virus in Belgium. We gratefully acknowledge two referees and an associate editor for provoking thoughts that have led to an improved version of the manuscript. This work was based on a serum sample collected for the European Commission's ESEN2-project. We are grateful to the Institute of Public Health, Brussels (Dr Robert Vranckx, Dr Veronik Hutse) for assistance with PVB19 testing. This work is part of the research project MSM 0021620839 that has been funded by 'SIMID', a strategic basic research project funded by the institute for the Promotion of Innovation by Science and Technology in Flanders, project number 060081, by the Fund of Scientific Research (Research Grant G039304) in Flanders, Belgium, by the IAP research network number P6/03 of the Belgian Government (Belgian Science Policy) and by the Grant Agency of Charles University, project number 252387/2007. This work benefited from discussions held in POLYMOD, a European Commission project funded within the Sixth Framework Programme, contract number: SSP22-CT-2004-502084.

Informal, interpersonal communication within a community about HIV and AIDS, or lack of such communication, may influence community members’ uptake of voluntary counseling and testing. Drawing from Noelle-Neumann’s spiral of silence theory, this study examined the association between communication about HIV/AIDS and prior HIV testing in communities in Tanzania, Zimbabwe, South Africa, and Thailand. Participants (N = 14,818) in 48 communities across five sites throughout the four countries completed a behavioral survey assessing communication, prior voluntary counseling and testing (VCT) uptake, social norms, stigma, and sexual risk. Site-specific logistic regression models demonstrated that frequent conversations about HIV were significantly associated with prior HIV testing at every site. Odds ratios for each site ranged from 1.885 to 3.085, indicating a roughly doubled or tripled chance of past VCT uptake. Results indicate that verbal communication may be an important mechanism for increasing health behaviors and inclusion in future interventions should be considered.

Zimbabwe’s HIV epidemic is amongst the worst in the world, and disproportionately effects poorer rural areas. Access to almost all health services in Zimbabwe includes some form of cost to the client. In recent years, the socio-economic and employment status of many Zimbabweans has suffered a serious decline, creating additional barriers to HIV treatment and care. We aimed to assess the impact of i) socio-economic status (SES) and ii) employment status on the utilization of health services in rural Zimbabwe. Data were collected from a random probability sample household survey conducted in the Mutoko district of north-western Zimbabwe in 2005. We selected variables that described the economic status of the respondent, including: being paid to work, employment status, and SES by assets. Respondents were also asked about where they most often utilized healthcare when they or their family was sick or hurt. Of 2,874 respondents, all forms of healthcare tended to be utilized by those of high or medium-high SES (65%), including private (65%), church-based (61%), traditional (67%), and other providers (66%) (P=0.009). Most respondents of low SES utilized government providers (74%) (P=0.009). Seventy-one percent of respondents utilizing health services were employed. Government (71%), private (72%), church (71%), community-based (78%) and other (64%) health services tended to be utilized by employed respondents (P=0.000). Only traditional health services were equally utilized by unemployed respondents (50%) (P=0.000). A wide range of health providers are utilized in rural Zimbabwe. Utilization is strongly associated with SES and employment status, particularly for services with user fees, which may act as a barrier to HIV treatment and care access. Efforts to improve access in low-SES, high HIV-prevalence settings may benefit from the subsidization of the health care payment system, efforts to improve SES levels, political reform, and the involvement of traditional providers.