In the framework of Object Oriented Data Analysis, a permutation approach to the two-sample testing problem for network-valued data is proposed. In detail, the present framework proceeds in four ...steps: (i) matrix representation of the networks, (ii) computation of the matrix of pairwise (inter-point) distances, (iii) computation of test statistics based on inter-point distances and (iv) embedding of the test statistics within a permutation test. The proposed testing procedures are proven to be exact for every finite sample size and consistent. Two new test statistics based on inter-point distances (i.e., IP-Student and IP-Fisher) are defined and a method to combine them to get a further inferential tool (i.e., IP-StudentFisher) is introduced. Simulated data shows that tests with our statistic exhibit a statistical power that is either the best or second-best but very close to the best on a variety of possible alternatives hypotheses and other statistics. A second simulation study that aims at better understanding which features are captured by specific combinations of matrix representations and distances is presented. Finally, a case study on mobility networks in the city of Milan is carried out. The proposed framework is fully implemented in the R package nevada (NEtwork-VAlued Data Analysis).
Networks are a natural way of representing the human brain for studying its structure and function and, as such, have been extensively used. In this framework, case–control studies for understanding ...autism pertain to comparing samples of healthy and autistic brain networks. In order to understand the biological mechanisms involved in the pathology, it is key to localize the differences on the brain network. Motivated by this question, we hereby propose a general non‐parametric finite‐sample exact statistical framework that allows to test for differences in connectivity within and between prespecified areas inside the brain network, with strong control of the family‐wise error rate. We demonstrate unprecedented ability to differentiate children with non‐syndromic autism from children with both autism and tuberous sclerosis complex using electroencephalography data. The implementation of the method is available in the R package nevada.
Motivated by the analysis of a dataset of ultrasound tongue profiles, we present multi-aspect interval-wise testing (IWT), i.e., a local nonparametric inferential technique for functional data ...embedded in Sobolev spaces. Multi-aspect IWT is a nonparametric procedure that tests differences between groups of functional data, jointly taking into account the curves and their derivatives. Multi-aspect IWT provides adjusted multi-aspect p-value functions that can be used to select intervals of the domain that are imputable for the rejection of a null hypothesis. As a result, it can impute the rejection of a functional null hypothesis to specific intervals of the domain and to specific orders of differentiation. We show that the multi-aspect p-value functions are provided with a control of the family-wise error rate and that they are consistent. We apply multi-aspect IWT to the analysis of a dataset of tongue profiles recorded for a study on Tyrolean, a German dialect spoken in South Tyrol. We test differences between five different ways of articulating the uvular /r/: vocalized /r/, approximant, fricative, tap, and trill. Multi-aspect IWT-based comparisons result in an informative and detailed representation of the regions of the tongue where a significant difference occurs.
Purpose:
Anastomotic pseudoaneurysms of transplanted kidneys are a very rare complication encountered in less than 1% of cases. They may be devastating, leading to functional impairment, kidney ...transplantectomy, or death. Treatment has not been standardized, with open surgical repair considered the safest procedure even if it is often complicated by bleeding and graft loss. The purpose of this case report is to describe an endovascular treatment of this condition, consisting of the combination of coil embolization and arterial stenting.
Case report:
A 61-year-old woman developed an anastomotic pseudoaneurysm 2 months after kidney transplantation, causing acute kidney injury related to ab-extrinsic stenosis of the transplant renal artery (TRA) and external iliac artery. The pseudoaneurysm was successfully treated by coil embolization, and the arterial patency was restored by the stenting of TRA and external iliac artery. The patient completely recovered kidney function, and after a 6-month-follow-up, creatinine values were stable with normal renal perfusion.
Conclusion:
Endovascular repair through coil embolization and TRA stenting can be a safe and effective option to treat anastomotic pseudoaneurysm in kidney transplant.
In many applications, process monitoring has to deal with functional responses, which are also known as profile data. In these scenarios, a relevant industrial problem consists of detecting faults by ...combining supervised learning with functional data analysis and statistical process monitoring. Supervised learning is usually applied to the whole signal domain, with the aim of discovering the features that are affected by the faults of interest. We explore a different perspective, which consists of performing supervised learning to select inferentially the parts of the signal data that are more informative in terms of underlying fault factors. The procedure is based on a non-parametric domain-selective functional analysis of variance and allows us to identify the specific subintervals where the profile is sensitive to process changes. Benefits achieved by coupling the proposed approach with profile monitoring are highlighted by using a simulation study. We show how applying profile monitoring only to the identified subintervals can reduce the time to detect the out-of-control state of the process. To illustrate its potential in industrial applications, the procedure is applied to remote laser welding, where the main aim is monitoring the gap between the welded plates through the observation of the emission spectra of the welded material.
The purpose of this paper is to provide an overview of available methods for reliability investigations when the outcome of interest is a curve. Curve data, or functional data, is commonly collected ...in biomechanical research in order to better understand different aspects of human movement. Using recent statistical developments, curve data can be analysed in its most detailed form, as functions. However, an overview of appropriate statistical methods for assessing reliability of curve data is lacking. A review of contemporary literature of reliability measures for curve data within the fields of biomechanics and statistics identified the following methods: coefficient of multiple correlation, functional limits of agreement, measures of distance and similarity, and integrated pointwise indices (an extension of univariate reliability measures to curve data, inclusive of Pearson correlation, intraclass correlation, and standard error of measurement). These methods are briefly presented, implemented (R-code available as supplementary material) and evaluated on simulated data to highlight advantages and disadvantages of the methods. Among the identified methods, the integrated intraclass correlation and standard error of measurement are recommended. These methods are straightforward to implement, enable results over the domain, and consider variation between individuals, which the other methods partly neglect.
We address the problem of finite-sample null hypothesis significance testing on the mean element of a random variable that takes value in a generic separable Hilbert space. For this purpose, we ...propose a (re)definition of Hotelling’s T2 that naturally expands to any separable Hilbert space that we further embed within a permutation inferential approach. In detail, we present a unified framework for making inference on the mean element of Hilbert populations based on Hotelling’s T2 statistic, using a permutation-based testing procedure of which we prove finite-sample exactness and consistency; we showcase the explicit form of Hotelling’s T2 statistic in the case of some famous spaces used in functional data analysis (i.e., Sobolev and Bayes spaces); we demonstrate, by means of simulations, that Hotelling’s T2 exhibits the best performances in terms of statistical power for detecting mean differences between Gaussian populations, compared to other state-of-the-art statistics, in most simulated scenarios; we propose a case study that demonstrate the importance of the space into which one decides to embed the data; we provide an implementation of the proposed tools in the R package fdahotelling available at https://github.com/astamm/fdahotelling.
The aim of this work is to introduce an approach to null hypothesis significance testing in a functional linear model for spatial data. The proposed method is capable of dealing with the spatial ...structure of data by building a permutation testing procedure on spatially filtered residuals of a spatial regression model. Indeed, due to the spatial dependence existing among the data, the residuals of the regression model are not exchangeable, breaking the basic assumptions of the Freedman and Lane permutation scheme. Instead, it is proposed here to estimate the variance–covariance structure of the residuals by variography, remove this correlation by spatial filtering residuals and base the permutation test on these approximately exchangeable residuals. A simulation study is conducted to evaluate the performance of the proposed method in terms of empirical size and power, examining its behavior under different covariance settings. We show that neglecting the residuals spatial structure in the permutation scheme (thus permuting the correlated residuals directly) yields a very liberal testing procedures, whereas the proposed procedure is close to the nominal size of the test. The methodology is demonstrated on a real world data set on the amount of waste production in the Venice province of Italy.
Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as componentwise inference for multivariate ...data naturally performs feature selection, subsetwise inference for functional data performs domain selection. In this paper, we present a unified testing framework for domain selection on populations of functional data. In detail, p‐values of hypothesis tests performed on pointwise evaluations of functional data are suitably adjusted for providing control of the familywise error rate (FWER) over a family of subsets of the domain. We show that several state‐of‐the‐art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined thresholdwise testing, in which the family of subsets is instead built in a data‐driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a priori defined families. We provide theoretical results with respect to consistency and control of the FWER for the methods within the unified framework. We illustrate the performance of the methods within the unified framework on simulated and real data examples and compare their performance with other existing methods.
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