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Araveeporn, Autcha. "Comparing the Linear and Quadratic Discriminant Analysis of Diabetes Disease Classification Based on Data Multicollinearity". International Journal of Mathematics and Mathematical Sciences 2022 (6.09.2022): 1–11. http://dx.doi.org/10.1155/2022/7829795.
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Linear and quadratic discriminant analysis are two fundamental classification methods used in statistical learning. Moments (MM), maximum likelihood (ML), minimum volume ellipsoids (MVE), and t-distribution methods are used to estimate the parameter of independent variables on the multivariate normal distribution in order to classify binary dependent variables. The MM and ML methods are popular and effective methods that approximate the distribution parameter and use observed data. However, the MVE and t-distribution methods focus on the resampling algorithm, a reliable tool for high resistance. This paper starts by explaining the concepts of linear and quadratic discriminant analysis and then presents the four other methods used to create the decision boundary. Our simulation study generated the independent variables by setting the coefficient correlation via multivariate normal distribution or multicollinearity, often through basic logistic regression used to construct the binary dependent variable. For application to Pima Indian diabetic dataset, we expressed the classification of diabetes as the dependent variable and used a dataset of eight independent variables. This paper aimed to determine the highest average percentage of accuracy. Our results showed that the MM and ML methods successfully used large independent variables for linear discriminant analysis (LDA). However, the t-distribution method of quadratic discriminant analysis (QDA) performed better when using small independent variables.
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Tucker, Larry A., Denise S. Demers i K. Patrick Kelly. "A Prediction Equation for Estimating Body Fat Percentage Using Readily Accessible Measures: A Multivariate Study of 200 Adult Women". American Journal of Health Promotion 12, nr 4 (marzec 1998): 229–36. http://dx.doi.org/10.4278/0890-1171-12.4.229.
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Purpose. This study was conducted to develop a regression equation that accurately estimates body fat percentage using relatively easy and inexpensive methods that do not require women to remove clothing. Design. A cross-sectional design was employed. Setting. All data were collected at the University. Subjects. Subjects were 200 white women ages 20 to 65 years. The sample was equally distributed across four age groups, 20–29, 30–39, 40–49, and 50–65, and within each age group, one-third of the women were lean, one-third were of average weight, and one-third were obese. Measures. Subjects were hydrostatically weighed and participated in a variety of anthropometric and lifestyle assessments, including skinfolds, circumferences, and questionnaire responses. Results. The full regression model included six measures: hip circumference, triceps skinfold (observed and quadratic), age (quadratic), self-reported physical activity, and calf skinfold (quadratic). This equation accounted for 81 % of the variance in body weight measured by hydrostatic weighing (SEE = 3.5%). A simpler, five-variable equation was also formed that did not include the calf skinfold assessment (R2 = .800, SEE = 3.6%). Conclusions. The prediction equations in this study afford accurate and relatively easy and inexpensive means of estimating body fat percentage in a wide range of white women without having them remove their clothing.
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Ochoa, Maicol, i Ignacio Cascos. "Data Depth and Multiple Output Regression, the Distorted M-Quantiles Approach". Mathematics 10, nr 18 (9.09.2022): 3272. http://dx.doi.org/10.3390/math10183272.
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For a univariate distribution, its M-quantiles are obtained as solutions to asymmetric minimization problems dealing with the distance of a random variable to a fixed point. The asymmetry refers to the different weights awarded to the values of the random variable at either side of the fixed point. We focus on M-quantiles whose associated losses are given in terms of a power. In this setting, the classical quantiles are obtained for the first power, while the expectiles correspond to quadratic losses. The M-quantiles considered here are computed over distorted distributions, which allows to tune the weight awarded to the more central or peripheral parts of the distribution. These distorted M-quantiles are used in the multivariate setting to introduce novel families of central regions and their associated depth functions, which are further extended to the multiple output regression setting in the form of conditional and regression regions and conditional depths.
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Jiang, Yixiao. "A Hausman Test for Partially Linear Models with an Application to Implied Volatility Surface". Journal of Risk and Financial Management 13, nr 11 (19.11.2020): 287. http://dx.doi.org/10.3390/jrfm13110287.
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This paper develops a test that helps assess whether the term structure of option implied volatility is constant across different levels of moneyness. The test is based on the Hausman principle of comparing two estimators, one that is efficient but not robust to the deviation being tested, and one that is robust but not as efficient. Distribution of the proposed test statistic is investigated in a general semiparametric setting via the multivariate Delta method. Using recent S&P 500 index traded options data from September 2009 to December 2018, we find that a partially linear model permitting a flexible “volatility smile” and an additive quadratic time effect is a statistically adequate depiction of the implied volatility data for most years. The constancy of implied volatility term structure, in turn, implies that option traders shall feel confident and execute volatility-based strategies using at-the-money options for its high liquidity.
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Araveeporn, Autcha. "Comparison of Logistic Regression and Discriminant Analysis for Classification of Multicollinearity Data". WSEAS TRANSACTIONS ON MATHEMATICS 22 (16.02.2023): 120–31. http://dx.doi.org/10.37394/23206.2023.22.15.
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The objective of this study is to concentrate on the classification method of the logistic regression and the discriminant analysis by using the simulation dataset and the liver patients as the actual data. These datasets are used the binary dependent variable depending on the correlated independent variables or called multicollinearity data. The standard classification method is logistic regression, which uses the logit function’s probability to conduct the dichotomous dependent variable. The iteration process can be solved to estimate logit function parameters and explain the relationship between a dependent binary variable and independent variables. Discriminant analysis is a powerful classification based on linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and regularized discriminant analysis (RDA). These methods consider the decision boundaries by building a classifier model on the multivariate normal distribution. LDA defines the standard covariance matrix, but QDA has an individual covariance matrix. RDA extends from QDA by setting the regularized parameter to estimate the covariance matrix. In the case of the simulation study, the independent variables are generated by defining the constant correlation on the multivariate normal distribution that made the multicollinearity problem. Then the binary response variable can be approximated from the logit function. For application to actual data, we expressed the classification of type liver and non-liver patients as the dependent variables and obtained patient personal information on the nine independent variables. The highest average percentage of accuracy determines the performance of these methods. The results have shown that the logistic regression was successful when using small independent variables, but the RDA performed when using large independent variables.
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Abd Almuhsen, Tahseen Ali, i Ahmed Jasim Sultan. "Coordination of directional overcurrent and distance relays based on nonlinear multivariable optimization". Indonesian Journal of Electrical Engineering and Computer Science 17, nr 3 (1.03.2020): 1194. http://dx.doi.org/10.11591/ijeecs.v17.i3.pp1194-1205.
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To ensure stability, security, and protection of electrical equipment from the damage the suitable coordination must be made in interconnected networks. In this paper, the nonlinear multivariable optimization techniques have been used with different performance indexes: Sequential quadratic programming (SQP), Sequential quadratic programming legacy (SQP-Legacy), Interior-Point and Active-Set for IEEE- 8 bus test system. This system consists of twenty-eight protective relays divided into fourteen directional overcurrent relays (DOCR) and fourteen distance relays (DR). It has been tested in the ETAP environment to obtain three-phase short circuit current at the near and far end faults and operating time for all DOC relays for near-end fault as well as test the second zone time for distance relays (TZ2) with pilot signal (WP)and without pilot signal (WOP) of the proposed algorithm was used to reduce overall operating time of DOC relays and obtain optimal values for time multiplier setting (TMS) and TZ2 with the different coordination time interval (CTI) between main and backup relays. The simulation results were validated in ETAP program prove that the effectiveness of the Active-Set to minimize the TMS and TZ2 for the system.<em> </em>
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Whalley, A., i M. Ebrahimi. "Robust Stability with System Uncertainties". Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216, nr 5 (1.05.2002): 495–508. http://dx.doi.org/10.1177/095440620221600501.
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Multivariable system models in the form of parameterized, impedance, matrix quadratic realizations are considered. System uncertainties in the form of mass-inertia or damping variations are acknowledged. Simple proportional controller models are proposed and the effect of model variations on the stability of the closed-loop system is investigated. Frequency domain methods are employed to predict the relative stability condition of the system. Conventional stability margin measures may be invoked while adjusting the controller design parameter to an appropriate setting.
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Kolankowski, Michał, i Robert Piotrowski. "Design of Three Control Algorithms for an Averaging Tank with Variable Filling". Acta Mechanica et Automatica 16, nr 2 (18.04.2022): 136–50. http://dx.doi.org/10.2478/ama-2022-0018.
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Abstract An averaging tank with variable filling is a nonlinear multidimensional system and can thus be considered a complex control system. General control objectives of such object include ensuring stability, zero steady-state error, and achieving simultaneously shortest possible settling time and minimal overshoot. The main purpose of this research work was the modeling and synthesis of three control systems for an averaging tank. In order to achieve the intended purpose, in the first step, a mathematical model of the control system was derived. The model was adapted to the form required to design two out of three planned control systems by linearization and reduction of its dimensions, resulting in two system variants. A multivariable proportional-integral-derivative (PID) control system for the averaging tank was developed using optimization for tuning PID controllers. State feedback and output feedback with an integral action control system for the considered control system was designed using a linear-quadratic regulator (LQR) and optimization of weights. A fuzzy control system was designed using the Mamdani inference system. The developed control systems were tested using theMATLAB environment. Finally, the simulation results for each control algorithm (and their variants) were compared and their performance was assessed, as well as the effects of optimization in the case of PID and integral control (IC) systems.
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Bernabe-Ortiz, Antonio, Rodrigo M. Carrillo-Larco i J. Jaime Miranda. "Association between body mass index and blood pressure levels across socio-demographic groups and geographical settings: analysis of pooled data in Peru". PeerJ 9 (21.04.2021): e11307. http://dx.doi.org/10.7717/peerj.11307.
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Background Understanding the relationship between BMI and blood pressure requires assessing whether this association is similar or differs across population groups. This study aimed to assess the association between body mass index (BMI) and blood pressure levels, and how these associations vary between socioeconomic groups and geographical settings. Methods Data from the National Demographic Health Survey of Peru from 2014 to 2019 was analyzed considering the complex survey design. The outcomes were levels of systolic (SBP) and diastolic blood pressure (DBP), and the exposure was BMI. Exposure and outcomes were fitted as continuous variables in a non-linear quadratic regression model. We explored effect modification by six socioeconomic and geographical variables (sex, age, education level, socioeconomic position, study area, and altitude), fitting an interaction term between each of these variables and BMI. Results Data from 159, 940 subjects, mean age 44.4 (SD: 17.1), 54.6% females, was analyzed. A third (34.0%) of individuals had ≥12 years of education, 24.7% were from rural areas, and 23.7% lived in areas located over 2,500 m above sea level. In the overall sample mean BMI was 27.1 (SD: 4.6) kg/m2, and mean SBP and DBP were 122.5 (SD: 17.2) and 72.3 (SD: 9.8) mmHg, respectively. In the multivariable models, greater BMI levels were associated with higher SBP (p-value < 0.001) and DBP (p-value < 0.001). There was strong evidence that sex, age, education level, and altitude were effect modifiers of the association between BMI and both SBP and DBP. In addition to these socio-demographic variables, socioeconomic position and study area were also effect modifiers of the association between BMI and DBP, but not SBP. Conclusions The association between BMI and levels of blood pressure is not uniform on a range of socio-demographic and geographical population groups. This characterization can inform the understanding of the epidemiology and rise of blood pressure in a diversity of low-resource settings.
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Pallegedara, Asankha. "Food consumption choice and demand by the Sri Lankan households". Journal of Agribusiness in Developing and Emerging Economies 9, nr 5 (14.10.2019): 520–35. http://dx.doi.org/10.1108/jadee-01-2019-0014.
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Purpose Food consumption patterns have changed in many Asian countries over the past two–three decades. It is important to understand the changes in food consumption patterns and its drivers in different country settings as each country has different food cultures, tastes and habits. Thus, the purpose of this paper is to examine the patterns and determinants of food consumption choice and demand in Sri Lanka. Design/methodology/approach Using Household Income and Expenditure Survey 1990/1991, 2002 and 2012/2013 data, this study explores the relationship between food consumption patterns and the observed changes reported in per capita income, urbanization, structural transformations and demographics. Specifically, present study estimates the probability of consuming main food items such as rice, bread, dhal, vegetables and fish using a multivariate probit model and also estimates income and price elasticities of household major food items by applying Quadratic Almost Ideal Demand System. Findings This study demonstrates that per capita income, food prices, education level of the household heads, rural–urban affiliation and ethnic background significantly affect the consumption decision of the major food items. Sri Lankan households in general seem to consider that rice and dhal are necessary commodities, whereas bread and fish are luxury commodities. Research limitations/implications The lack of panel data and several missing districts in two survey rounds for analysis are limitations of the study. Originality/value To the author’s knowledge, this is the first study for Sri Lanka that examines food consumption choice and demand using nationwide data for the last two decades. This study applies novel econometric techniques to account for various issues in data analysis.
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Seres, István András, Máté Horváth i Péter Burcsi. "The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications". Applicable Algebra in Engineering, Communication and Computing, 1.03.2023. http://dx.doi.org/10.1007/s00200-023-00599-2.
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AbstractSequences of consecutive Legendre and Jacobi symbols as pseudorandom bit generators were proposed for cryptographic use in 1988. Major interest has been shown towards pseudorandom functions (PRF) recently, based on the Legendre and power residue symbols, due to their efficiency in the multi-party setting. The security of these PRFs is not known to be reducible to standard cryptographic assumptions. In this work, we show that key-recovery attacks against the Legendre PRF are equivalent to solving a specific family of multivariate quadratic (MQ) equation system over a finite prime field. This new perspective sheds some light on the complexity of key-recovery attacks against the Legendre PRF. We conduct algebraic cryptanalysis on the resulting MQ instance. We show that the currently known techniques and attacks fall short in solving these sparse quadratic equation systems. Furthermore, we build novel cryptographic applications of the Legendre PRF, e.g., verifiable random function and (verifiable) oblivious (programmable) PRFs.
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Kuc, Joanna, Hannes Kettner, Fernando Rosas, David Erritzoe, Eline Haijen, Mendel Kaelen, David Nutt i Robin L. Carhart-Harris. "Psychedelic experience dose-dependently modulated by cannabis: results of a prospective online survey". Psychopharmacology, 4.11.2021. http://dx.doi.org/10.1007/s00213-021-05999-1.
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Abstract Rationale. Classic psychedelics are currently being studied as novel treatments for a range of psychiatric disorders. However, research on how psychedelics interact with other psychoactive substances remains scarce. Objectives The current study aimed to explore the subjective effects of psychedelics when used alongside cannabis. Methods Participants (n = 321) completed a set of online surveys at 2 time points: 7 days before, and 1 day after a planned experience with a serotonergic psychedelic. The collected data included demographics, environmental factors (so-called setting) and five validated questionnaires: Mystical Experience Questionnaire (MEQ), visual subscales of Altered States of Consciousness Questionnaire (ASC-Vis), Challenging Experience Questionnaire (CEQ), Ego Dissolution Inventory (EDI) and Emotional Breakthrough Inventory (EBI). Participants were grouped according to whether they had reported using no cannabis (n = 195) or low (n = 53), medium (n = 45) or high (n = 28) dose, directly concomitant with the psychedelic. Multivariate analysis of covariance (MANCOVA) and contrasts was used to analyse differences in subjective effects between groups while controlling for potential confounding contextual ‘setting’ variables. Results The simultaneous use of cannabis together with classic serotonergic psychedelics was associated with more intense psychedelic experience across a range of measures: a linear relationship was found between dose and MEQ, ASC-Vis and EDI scores, while a quadratic relationship was found for CEQ scores. No relationship was found between the dose of cannabis and the EBI. Conclusions Results imply a possible interaction between the cannabis and psychedelic on acute subjective experiences; however, design limitations hamper our ability to draw firm inferences on directions of causality and the clinical implications of any such interactions.
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Dey, Debangan, Abhirup Datta i Sudipto Banerjee. "Graphical Gaussian process models for highly multivariate spatial data". Biometrika, 4.12.2021. http://dx.doi.org/10.1093/biomet/asab061.
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Summary For multivariate spatial Gaussian process models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence between the variables. This is undesirable, especially in highly multivariate settings, where popular cross-covariance functions, such as multivariate Matérn functions, suffer from a curse of dimensionality as the numbers of parameters and floating-point operations scale up in quadratic and cubic order, respectively, with the number of variables. We propose a class of multivariate graphical Gaussian processes using a general construction called stitching that crafts cross-covariance functions from graphs and ensures process-level conditional independence between variables. For the Matérn family of functions, stitching yields a multivariate Gaussian process whose univariate components are Matérn Gaussian processes, and which conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Matérn Gaussian process to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling.
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Harman, Radoslav, i Mária Trnovská. "Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices". Mathematica Slovaca 59, nr 6 (1.01.2009). http://dx.doi.org/10.2478/s12175-009-0157-9.
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AbstractIn the paper we solve the problem of D ℋ-optimal design on a discrete experimental domain, which is formally equivalent to maximizing determinant on the convex hull of a finite set of positive semidefinite matrices. The problem of D ℋ-optimality covers many special design settings, e.g., the D-optimal experimental design for multivariate regression models. For D ℋ-optimal designs we prove several theorems generalizing known properties of standard D-optimality. Moreover, we show that D ℋ-optimal designs can be numerically computed using a multiplicative algorithm, for which we give a proof of convergence. We illustrate the results on the problem of D-optimal augmentation of independent regression trials for the quadratic model on a rectangular grid of points in the plane.
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Silva, Luiz Ricardo Trajano da, Victor Augusto Fernandes de Campos i Alain Segundo Potts. "Robust Control for Helicopters Performance Improvement: an LMI Approach". Journal of Aerospace Technology and Management, nr 12 (10.08.2020). http://dx.doi.org/10.5028/jatm.v12.1179.
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This paper presents an LMI (Linear Matrix Inequalities) application for the design of robust controllers for multivariate systems that have multiple points of operation. Some systems change their parameters along time, then, it is necessary to switch the control for different operational points. The purpose of this controller is to ensure the stability and performance requirements of the system for different operating points with the same controller. The method uses the following concepts of predefined structures controller, LMI region, and polytopic systems. To validate the controller a linearized model of a helicopter was used. These helicopters belong to a system class of MIMO (Multiple-Input Multiple Outputs) type and present a complex dynamic in their flight modes, therefore, due to these features, this type of helicopter is a good model to implement and test the efficiency of the described method in this work. The results were satisfactory. Some limitations in its implementation were found and discussed. An LQG (Linear-Quadratic-Gaussian) controller was also designed for the same model of the helicopter just for comparison. Analyzing the settling time properties, the LMI controller presented a better response than the LQG controller.
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Vu, Thanh-Huyen T., Linda Van Horn, Martha L. Daviglus, Queenie Chan, Alan R. Dyer, Victor W. Zhong, Rachel Gibson, Paul Elliott i Jeremiah Stamler. "Association between egg intake and blood pressure in the USA: the INTERnational study on MAcro/micronutrients and blood Pressure (INTERMAP)". Public Health Nutrition, 2.08.2021, 1–9. http://dx.doi.org/10.1017/s1368980021002949.
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Abstract Objectives: To investigate associations of egg intake with blood pressure (BP) and the role of dietary variables and other macro- and micro-nutrients in the association. Design: We used cross-sectional data for the USA as part of the INTERnational study on MAcro/micronutrients and blood Pressure (INTERMAP). INTERMAP was surveyed between 1996 and 1999, including four 24-h dietary recalls, two 24-h urine collections and eight measurements of systolic BP and diastolic BP (SBP, DBP). Average egg intake (g/d) was calculated. Multivariable linear regression models were used to estimate the association between egg intake (per each 50 g/d or per quintile) and BP. The roles of dietary variables and other macro- and micro-nutrients in this association were also investigated. Setting: In the USA. Participants: In total, 2195 US INTERMAP men and women aged 40–59 years. Results: Participants were 50 % female, 54 % non-Hispanic White and 16 % non-Hispanic Black. Mean egg intake (sd) in men and women was 30·4(29·8) and 21·6(20·5) g/d, respectively. Adjusting for demographics, socio-economics, lifestyle and urinary Na:K excretion ratios, we found non-linear associations with BP in non-obese women (P-quadratic terms: 0·004 for SBP and 0·035 for DBP).The associations remained after adjusting for dietary variables, macro/micro nutrients or minerals. Dietary cholesterol was highly correlated with egg intake and may factor in the association. No association was found in obese women and in obese or non-obese men. Conclusion: Egg intake was non-linearly associated with SBP and DBP in non-obese women, but not in obese women or men. Underlying mechanisms require additional study regarding the role of obesity and sex.