Multivariate Statistical Inference Research Articles

Typology analysis and adaptive capacity of commercial gardening farmers to climate change in peri-urban areas along the coastal area of Benin (West Africa)

The coastal environment represents a special site for human and economic activities. The population growth in this area has led to strong urbanization and, therefore, to the establishment of small-scale vegetable farms to feed the growing urban and peri-urban populations. This is an opportunity for youth employment and reduce poverty as this activity generates reliable incomes. However, in recent years, climatic changes and rapid urbanization have influenced agricultural activities in this area. The aim of this study was to characterize market gardening systems along the coastal area of Benin and understand farmers’ perceptions and adaptation strategies in response to the ongoing environmental changes. Data was collected from 130 farms using individual semi-structured questionnaires. A principal component analysis (PCA), K-Mean multivariate classification and statistical inference were used for data analysis. Three farm groups were identified from the hierarchical bottom-up classification: modern coastal farms (MCF, 59.24%), small-scale intra-urban farms (SIF, 35.38%) and traditional co-managed lowland farms (TCF, 5.38%). The perceived environmental changes were mainly temperature increases, strong winds and migration to another farmland. The criteria differentiating the groups were strong winds and variation in the start date of the rains (p < 0.05). According to current strategies farmers in groups 1 and 2 preferred crop diversification, those in group 3 moved their farms. Future strategies range from the early sale of crops to the use of modern watering equipment to the cessation of farming. Thus, sustainable farm management requires the involvement of decentralized structures and local stakeholders to maintain the livelihoods of local populations.

A robust test approach for equality of mean vectors of two independent groups under the multivariate Behrens-Fisher problem

In multivariate statistical inference, the Hotelling T 2 statistic is used to test the equality of mean vectors for two independent groups. This statistic needs the multivariate normality and homogeneous covariance matrices assumptions. However, homogeneous covariance matrices assumption may not be provided in real applications. This case is called the multivariate Behrens-Fisher problem. There are several studies to test the equality of two mean vectors for the independent groups under the multivariate Behrens-fisher problem. But these studies do not interest in outliers at data sets. In this study, we propose solving problems caused by multivariate Behrens-Fisher and outliers in the dataset. We compare our proposed approach with other approaches regarding empirical size and power at simulated data that are both uncontaminated and contaminated. Thus we show that our proposed approach can be used to test the equality of mean vectors for two independent groups under multivariate Behrens-Fisher problem without being affected by outliers in the data. Moreover, we construct an R function in the MVTests package to use our proposed approach for real data applications.

Uncovering Diverse Mechanistic Spreading Pathways in Disease Progression of Alzheimer's Disease.

The AT[N] research framework focuses on three major biomarkers in Alzheimer's disease (AD): amyloid-β deposition (A), pathologic tau (T), and neurodegeneration [N]. We hypothesize that the diverse mechanisms such as A⟶T and A⟶[N] pathways from one brain region to others, may underlie the wide variation in clinical symptoms. We aim to uncover the causal-like effect of regional AT[N] biomarkers on cognitive decline as well as the interaction with non-modifiable risk factors such as age and APOE4. We apply multi-variate statistical inference to uncover all possible mechanistic spreading pathways through which the aggregation of an upstream biomarker (e.g., increased amyloid level) in a particular brain region indirectly impacts cognitive decline, via the cascade build-up of a downstream biomarker (e.g., reduced metabolism level) in another brain region. Furthermore, we investigate the survival time for each identified region-to-region pathological pathway toward the AD onset. We have identified a collection of critical brain regions on which the amyloid burdens exert an indirect effect on the decline in memory and executive function (EF) domain, being mediated by the reduction of metabolism level at other brain regions. APOE4 status has been found not only involved in many A⟶N mechanistic pathways but also significantly contributes to the risk of developing AD. Our major findings include 1) the region-to-region A⟶N⟶MEM and A⟶N⟶MEM pathways exhibit distinct spatial patterns; 2) APOE4 is significantly associated with both direct and indirect effects on the cognitive decline while sex difference has not been identified in the mediation analysis.

Ocena zmian komponentów wskaźnika NEET w krajach Unii Europejskiej z zastosowaniem testu T2 Hotellinga

Decision-makers and researchers dealing with labour market and education are largely focused on the NEET rate of young people as an indicator complementary to the unemployment rate. Typically in studies, it is the change in the overall NEET rate of young people that is evaluated, rather than changes in its individual components. The aim of the study presented in this paper is to detect the volume of changes in the components of the NEET rate determined on the basis of socio-demographic and economic features of young people in EU countries, by means of Hotelling’s T2 test for dependent measurements. The study employed multivariate statistical inference, and more specifically, the multiple comparison tests. The analysis covered the years 2019 and 2021, i.e. the year preceding the outbreak of the COVID-19 pandemic and the full year of its duration. The calculations were performed on the data drawn from the Eurostat database. The study demonstrates that the comparison of the NEET youth rate components allows a more detailed assessment of the change in the labout market situation of young people belonging to this category than comparing the overall NEET rates only. For this reason, it would be advisable to apply a multidimensional approach when making decisions concerning labour market policies.

Uncovering Diverse Mechanistic Spreading Pathways in Disease Progression of Alzheimer's Disease

AbstractBackgroundAlthough the root cause of Alzheimer's disease (AD) is largely elusive, the amyloid hypothesis has been widely used in the AD research framework, where amyloidosis induces (A biomarker) or facilitates the spread of pathologic tau (T biomarker) followed by immediate neurodegeneration ([N] biomarker) and progressive cognitive decline. As the massive heterogeneities manifested in the clinical symptoms, it is critical to understand the pathophysiological mechanism of how whole‐brain AT[N] biomarkers exert a synergistic effect on cognitive decline in the long period of disease progression.MethodTo answer this important scientific question, we employ a novel multivariate statistical inference approach to uncover the causal‐like effect of AT[N] biomarkers on cognitive decline as well as the underlying non‐modifiable risk factors through high‐dimensional neuroimaging phenotypes. Specifically, we first present a multivariate variable selection method to identify a set of brain regions where the AT[N] biomarkers exhibit strong correlations to the clinical outcomes, such as the composite scores regarding memory or executive function domains. Next, we apply mediation analysis to uncover all possible mechanistic spreading pathways of AT[N] biomarkers that lead to cognitive decline. On top of this, we further investigate the survival time for each identified (either direct or mediated) pathological pathway toward the onset of clinical symptoms, which allows us to manage the priority of risk factors more effectively in routine clinical practice.Result(1) There are several brain regions on which the amyloid burdens exert an indirect effect on cognitive decline, being mediated by the reduction of metabolism level at other topologically connected brain regions. (2) There is no overlap between memory‐specific and EF (executive function)‐specific pathways in terms of involved brain region. (3) Having two APOE ε4 alleles significantly increases the risk of developing AD in our survival model, where the odds ratio is 0.474 (p‐value: 0.01) regarding memory problem and 0.60 (p‐value: 0.002) for decline of executive functions.ConclusionWe have identified a set of mechanistic pathways in the brain where AT[N] biomarkers from multiple regions exert synergistic effect to cognitive decline. The survival rates estimated on these pathways set the stage for the precision medicine in AD treatment.

Decoding with confidence: Statistical control on decoder maps

In brain imaging, decoding is widely used to infer relationships between brain and cognition, or to craft brain-imaging biomarkers of pathologies. Yet, standard decoding procedures do not come with statistical guarantees, and thus do not give confidence bounds to interpret the pattern maps that they produce. Indeed, in whole-brain decoding settings, the number of explanatory variables is much greater than the number of samples, hence classical statistical inference methodology cannot be applied. Specifically, the standard practice that consists in thresholding decoding maps is not a correct inference procedure. We contribute a new statistical-testing framework for this type of inference. To overcome the statistical inefficiency of voxel-level control, we generalize the Family Wise Error Rate (FWER) to account for a spatial tolerance δ, introducing the δ-Family Wise Error Rate (δ-FWER). Then, we present a decoding procedure that can control the δ-FWER: the Ensemble of Clustered Desparsified Lasso (EnCluDL), a procedure for multivariate statistical inference on high-dimensional structured data. We evaluate the statistical properties of EnCluDL with a thorough empirical study, along with three alternative procedures including decoder map thresholding. We show that EnCluDL exhibits the best recovery properties while ensuring the expected statistical control.

Research on the Quality Evaluation Strategy of Multi-source Heterogeneous Aggregation Data

In the era of big data, the application of multi-source heterogeneous aggregation data is more and more extensive. If the quality of aggregation data is uneven, it will bring a lot of troubles to the subsequent data mining, and then lead to inaccurate decision-making. A comprehensive quality evaluation method for aggregation data is proposed in this paper, based on factor analysis and multivariate variance analysis which is from the perspective of multivariate statistical inference. The case study shows that the method proposed in this paper is feasible and adaptive for the long-term evaluation of the quality of multi-source heterogeneous aggregation data.

A revision of Kerivoula hardwickii and occurrence of K. furva (Chiroptera: Vespertilionidae) in China.

Although increased survey efforts using improved capture methods (particularly harp traps) have greatly expanded the quantity of Kerivoula specimens available in China, the understanding of the genus has been long constrained. After the recently published revision of the hardwickii-complex with the description of K. furva and re-evaluation of occurrence of K. titania in Taiwan, the critical overview of the previous data of Chinese Kerivoula (with the exception of K. picta, a strikingly colored and unmistakable species) is imperative. To clarify the taxonomy and distribution of the hardwickii-complex in China, 40 additional specimens collected from South China were studied through detailed morphological comparisons, multivariate statistical methods and phylogenetic inference. Our results evidently classified these specimens as K. furva instead of K. titania or K. hardwickii sensu stricto and together with the critical review of literature data indicate that all previous Chinese records of the two latter species were based on either misidentifications or outdated taxonomy. K. furva have so far been recorded in the Chinese provinces of Chongqing, Fujian, Guangdong, Guangxi, Hainan, Hunan, Jiangxi, Yunnan and Taiwan, but more field surveys are needed to confirm whether it could be found in other nearby provinces.

Estimation of the asymptotic variance of univariate and multivariate random fields and statistical inference

Correlated random fields are a common way to model dependence structures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymptotic variance which adds up all autocovariances in the temporal and spatial domain. Especially, it arises in the standardization of test statistics based on partial sums of random fields and thus the construction of tests requires its estimation. In this paper we propose consistent estimators for this parameter for strictly stationary $\varphi $-mixing random fields with arbitrary dimension of the domain and taking values in a Euclidean space of arbitrary dimension, thus allowing for multivariate random fields. We establish consistency, provide central limit theorems and show that distributional approximations of related test statistics based on sample autocovariances of random fields can be obtained by the subsampling approach. As in applications the spatial-temporal correlations are often quite local, such that a large number of autocovariances vanish or are negligible, we also investigate a thresholding approach where sample autocovariances of small magnitude are omitted. Extensive simulation studies show that the proposed estimators work well in practice and, when used to standardize image test statistics, can provide highly accurate image testing procedures. Having in mind automatized applications on a big data scale as arising in data science problems, these examinations also cover the proposed data-adaptive procedures to select method parameters.

Multivariate statistical inference in a radial basis function neural network

Regression models and analysis of variance are widely used methods for analyzing manufacturing processes in the industry. Its objective is to analyze the effect of process input variables on a final quality characteristic. However, some processes have complex data that cannot be described by linear regression or have several product quality characteristics to be controlled, having several correlated responses makes it difficult to analyze and optimize the process, thus, it is common to ignore the correlation between responses and make several independent models for each response, causing problems for decision-making based on these models. This paper shows the application of multivariate statistical analysis in a Radial Basis Function neural network, considering the statistical significance between independent and dependent variables and the correlation and verifying if the assumptions for this analysis are fulfilled. The results evidence that the multivariate statistical analysis in the Radial Basis Function is a good method to analyze the process based on correlated variables: it satisfies the assumptions required for this analysis, it determines the process variation, and it also determines the most important variable that had influence in the process used to evaluate the permanent mold casting process.

Changes and classification in myocardial contractile function in the left ventricle following acute myocardial infarction

In this research, we hypothesized that novel biomechanical parameters are discriminative in patients following acute ST-segment elevation myocardial infarction (STEMI). To identify these biomechanical biomarkers and bring computational biomechanics ‘closer to the clinic’, we applied state-of-the-art multiphysics cardiac modelling combined with advanced machine learning and multivariate statistical inference to a clinical database of myocardial infarction. We obtained data from 11 STEMI patients (ClinicalTrials.gov NCT01717573) and 27 healthy volunteers, and developed personalized mathematical models for the left ventricle (LV) using an immersed boundary method. Subject-specific constitutive parameters were achieved by matching to clinical measurements. We have shown, for the first time, that compared with healthy controls, patients with STEMI exhibited increased LV wall active tension when normalized by systolic blood pressure, which suggests an increased demand on the contractile reserve of remote functional myocardium. The statistical analysis reveals that the required patient-specific contractility, normalized active tension and the systolic myofilament kinematics have the strongest explanatory power for identifying the myocardial function changes post-MI. We further observed a strong correlation between two biomarkers and the changes in LV ejection fraction at six months from baseline (the required contractility (r = − 0.79, p < 0.01) and the systolic myofilament kinematics (r = 0.70, p = 0.02)). The clinical and prognostic significance of these biomechanical parameters merits further scrutinization.

On Evaluation of Ensemble Forecast Calibration Using the Concept of Data Depth

Abstract Various generalizations of the univariate rank histogram have been proposed to inspect the reliability of an ensemble forecast or analysis in multidimensional spaces. Multivariate rank histograms provide insightful information about the misspecification of genuinely multivariate features such as the correlation between various variables in a multivariate ensemble. However, the interpretation of patterns in a multivariate rank histogram should be handled with care. The purpose of this paper is to focus on multivariate rank histograms designed based on the concept of data depth and outline some important considerations that should be accounted for when using such multivariate rank histograms. To generate correct multivariate rank histograms using the concept of data depth, the datatype of the ensemble should be taken into account to define a proper preranking function. This paper demonstrates how and why some preranking functions might not be suitable for multivariate or vector-valued ensembles and proposes preranking functions based on the concept of simplicial depth that are applicable to both multivariate points and vector-valued ensembles. In addition, there exists an inherent identifiability issue associated with center-outward preranking functions used to generate multivariate rank histograms. This problem can be alleviated by complementing the multivariate rank histogram with other well-known multivariate statistical inference tools based on rank statistics such as the depth-versus-depth (DD) plot. Using a synthetic example, it is shown that the DD plot is less sensitive to sample size compared to multivariate rank histograms.

Detection of structural changes through principal component analysis and multivariate statistical inference

This article introduces a new methodology for the detection of structural changes using a statistical data-driven modeling approach by means of a distributed piezoelectric active sensor network at different actuation phases. The three main features that characterize the proposed methodology are (a) the nature of the data used in the test since vectors of principal component analysis projections are used instead of the entire measured response of the structure or the coefficients of an AutoRegressive model, (b) the number of data used since the test is based on two random samples instead of some characteristic indicators, and (c) the samples come from a multidimensional variable and therefore a test for the plausibility of a value for a normal population mean vector is performed. The framework of multivariate statistical inference is used with the objective of the classification of structures in healthy or damaged. The novel scheme for damage detection presented in this article —based on multivariate inference over the principal component analysis projections of the raw data—is applied, validated, and tested on a small aluminum plate. The results show that the presented methodology is able to accurately detect damages, that is, for each actuation phase, a unique and reliable damage detection indicator is obtained no matter the number of sensors and/or actuators. It is worth noting that a major contribution of this article is that there exists an entire range of significance levels where the multivariate statistical inference is able to offer a correct decision although all of the univariate tests make a wrong decision.

Identification of Malaria-Infected Red Blood Cells Via Digital Shearing Interferometry and Statistical Inference

Malaria is one of the most widespread diseases, particularly in Asia and Africa. Correct diagnosis of malaria is necessary for its proper treatment. A compact automated tool for malaria identification will greatly benefit healthcare professionals in these regions. We propose a method that has the potential to automatically detect malaria-infected red blood cells (RBCs). This method combines the simplicity and robustness of lateral shearing interferometry with the flexibility of statistical methods to achieve the classification of diseased RBCs. Shearing interferograms generated using a glass plate in a common path setup were Fourier analyzed to retrieve the gradient phase and amplitude information of the cell. Then, multiple features based on the complex amplitude information of the cells are measured automatically and used to differentiate healthy and malaria-infected cells. Multivariate statistical inference algorithm of the experimental data shows that there is a difference between the populations of healthy and malaria-infected RBCs by using the measured RBC features.

Detection of event‐related modulations of oscillatory brain activity with multivariate statistical analysis of MEG data

We describe a method to detect brain activation in cortically constrained maps of current density computed from magnetoencephalography (MEG) data using multivariate statistical inference. We apply time-frequency (wavelet) analysis to individual epochs to produce dynamic images of brain signal power on the cerebral cortex in multiple time-frequency bands. We form vector observations by concatenating the power in each frequency band, and fit them into separate multivariate linear models for each time band and cortical location with experimental conditions as predictor variables. The resulting Roy's maximum root statistic maps are thresholded for significance using permutation tests and the maximum statistic approach. A source is considered significant if it exceeds a statistical threshold, which is chosen to control the familywise error rate, or the probability of at least one false positive, across the cortical surface. We compare and evaluate the multivariate approach with existing univariate approaches to time-frequency MEG signal analysis, both on simulated data and experimental data from an MEG visuomotor task study. Our results indicate that the multivariate method is more powerful than the univariate approach in detecting experimental effects when correlations exist between power across frequency bands. We further describe protected F-tests and linear discriminant analysis to identify individual frequencies that contribute significantly to experimental effects.

Samuel Stanley Wilks (1906–1964)

This article recalls and comments on the varied contributions, many of enduring value, made by Samuel Wilks to the theory and practice of statistics. Multivariate analysis, order statistics, and statistical inference have especially benefited from his research. His unflagging work on behalf of the profession as teacher, writer, editor, advisor, and committee member raised the visibility of the field of statistics and increased recognition of its wide relevance.

Multivariate statistical inference and applications

Some Properties of Random Vectors and Matrices. The Multivariate Normal Distribution. Hotelling's T -Tests. Multivariate Analysis of Variance. Discriminant Functions for Descriptive Group Separation. Classification of Observations into Groups. Multivariate Regression. Canonical Correlation. Principal Component Analysis. Factor Analysis. Appendices. Bibliography. Index.

Takesi Hayakawa, Makoto Aoshima, Kunio Shimizu (editors): MSI‐2000: Multivariate Statistical Analysis in Honor of Professor Minoru Siotani on his 70th Birthday. Volumes I and II of Proceedings of the Multivariate Statistical Inference 2000 Conference, also issued as no. 3 and 4 of vol. 15 (1995) and no. 1 and 2 of vol. 16 (1996) of the American Journal of Mathematical

Biometrical JournalVolume 39, Issue 7 p. 776-776 Book Review Takesi Hayakawa, Makoto Aoshima, Kunio Shimizu (editors): MSI-2000: Multivariate Statistical Analysis in Honor of Professor Minoru Siotani on his 70th Birthday. Volumes I and II of Proceedings of the Multivariate Statistical Inference 2000 Conference, also issued as no. 3 and 4 of vol. 15 (1995) and no. 1 and 2 of vol. 16 (1996) of the American Journal of Mathematical and Management Sciences, 270 and 238 pp., American Sciences Press, Syracuse, 1995, 1996, $ 125,— each Ekkehard Glimm, Ekkehard GlimmSearch for more papers by this author Ekkehard Glimm, Ekkehard GlimmSearch for more papers by this author First published: 18 January 2007 https://doi.org/10.1002/bimj.4710390704AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume39, Issue71997Pages 776-776 RelatedInformation

Optimum detection of multiple vapor materials with frequency-agile lidar

Differential absorption lidar (DIAL) is a well-established technology for estimating the concentration and its path integral CL of vapor materials using two closely spaced wavelengths. The recent development of frequency-agile lasers (FAL's) with as many as 60 wavelengths that can be rapidly scanned motivates the need for detection and estimation algorithms that are optimal for lidar employing these new sources. I derive detection and multimaterial CL estimation algorithms for FAL applications using the likelihood ratio test methodology of multivariate statistical inference theory. Three model sets of assumptions are considered with regard to the spectral properties of the backscatter from either topographic or aerosol targets. The calculations are illustrated through both simulated and actual lidar data.

The Heteroscedastic Method: Fifty+ Years of Progress 1945–2000, and Professor Minoru Siotani's Award-Winning Contributions

SYNOPTIC ABSTRACTIn this paper, we cover the genesis and development of the Heteroscedastic Method HM, with emphasis on the history (which can be regarded as starting in 1945, with some pre-history dating as far back as 1940), and only giving proofs insofar as needed to clarify ideas. As this paper is based on a Keynote Address to the Multivariate Statistical Inference 2000 (MSI2000) Conference in Honor of Professor Minoru Siotani held at the East-West Center, Honolulu, Hawaii, the fundamental contributions of Professor Siotani are given a focus in the discussion. Current and future research as we approach the year 2000 and beyond, and a time-line of development (past, present, and conjectured future) are also given.This research was supported by NATO Research Grant No. CRG 931030.