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Article
Statistics & Probability
Nesrin Guler et al.
Summary: This paper investigates the comparison problems of predictors between a linear mixed model and its transformed model, focusing on the covariance matrices of the best linear unbiased predictors. Various equalities and inequalities are established using inertia and rank formulas of block matrices. Results for special transformed models are also provided based on the findings for general cases.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Engineering, Multidisciplinary
Bo Jiang et al.
Summary: This paper addresses estimation, prediction, and inference problems on a linear random-effects model with linear restrictions on its parameter vector. The paper derives analytical formulas for the best linear unbiased predictors (BLUPs) and estimators (BLUEs), characterizes their mathematical and statistical properties, establishes various rank and inertia formulas for the covariance matrices, and presents necessary and sufficient conditions for equalities and inequalities of the covariance matrices.
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
(2023)
Article
Engineering, Multidisciplinary
Wenming Li et al.
Summary: This paper focuses on the comparison problems in statistical inference of two competing statistical models in regression analysis. The best linear unbiased estimators of unknown parameters under the two models are derived using precise matrix analytic tools. The statistical properties of the estimators are discussed, and the connections between the estimators under the two models are analyzed.
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
(2023)
Article
Mathematics, Applied
Yousef F. Alharbi et al.
Summary: By using the unified solver technique, new optical progressive and stationary structures, including hyperbolic, trigonometric, rational, periodical, and explosive types, have been established in stochastic nonlinear Schrodinger equations (NLSEs) with operative physical parameters. The obtained stochastic solutions with random parameters in the forms of rational, dissipative, explosive, envelope, periodic, and localized soliton can be applied in fiber applications. The stochastic modulations of structures' amplitude and frequency caused by fibers' nonlinear, dispersive, losing, and noise term effects may play a crucial role in new fiber communications.
Article
Mathematics, Interdisciplinary Applications
E. K. El-Shewy et al.
Summary: Multiple nonlinear plasma and burst electrostatic waves in magnetosphere and space show widely changing electric fields. The theory of stochastic-growth and density turbulence explains that localized fluctuations, damping, and electrostatic forcing occur. These plasma waves can be described by Schrodinger and Zakharov equations with stochastic terms, which are widely applicable to space plasma. Mathematical methods have produced new stochastic solutions for Zakharov model with noises in the subsonic limit. These solutions are important for studying electrostatic waves in aurora and solar-wind, including solitonic, breather, dark dissipative blow-up, explosive, shocks, and shock-like solitons. The effects of noise terms in Ito sense have been discussed, which may be useful for bursty waves in cusps regions and solar-wind.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Statistics & Probability
Nesrin Guler et al.
Summary: This paper explores the comparison problems for dispersion matrices of predictors in two competing linear models that have the same restrictions on their joint unknown parameters. One model is a constrained linear model (CLM), while the other model is a constrained over-parameterized model (COLM) obtained by adding new regressors to the CLM. By converting CLM and its COLM to their implicitly constrained forms, the authors provide analytical expressions and properties of the best linear unbiased predictors (BLUPs) using quadratic matrix optimization methods. The authors also derive equalities and inequalities for dispersion matrices of BLUPs under the models based on formulas of ranks and inertias of block matrices, and present comparison results for special cases.
STATISTICAL PAPERS
(2023)
Article
Mathematics, Interdisciplinary Applications
H. G. Abdelwahed et al.
Summary: This article presents the energy and wave dynamical features of the two-dimensional Maccari nonlinear system in fiber communications and modern physical science. It constructs new forms of solutions using a unified solver method, identifying new wave stochastic structures with important features in energy physics. The article also explores the role of random effects in modifying energy wave strength and collapsing due to model medium turbulence.
FRACTAL AND FRACTIONAL
(2023)
Article
Statistics & Probability
Melek Eris Buyukkaya
Summary: This work focuses on the dispersion matrices of best linear unbiased predictors (BLUPs) under linear mixed models (LMM) and reduced linear mixed models (RLMMs), aiming to establish analytical formulas for calculating their ranks and inertias.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2023)
Article
Statistics & Probability
Nesrin Guler
Summary: This study investigates a general linear random-effects model with both fixed and random effects, as well as its two transformed models. No restrictions are made on the correlation of random effects and any full rank assumptions. The focus is on establishing relationships and making comparisons between predictors under the two models.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2022)
Article
Mathematics
Nesrin Guler et al.
Summary: This paper discusses the comparison problems of predictor and estimator within SURMs, establishing equalities and inequalities for covariance matrices of BLUPs and OLSPs under various rank and inertia formulas of block matrices. The comparisons of BLUEs and OLSEs in the models are also considered in the results.
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Mahmoud A. E. Abdelrahman et al.
Summary: In this work, the exp(-phi(xi))-expansion method is applied to solve the deterministic and stochastic Phi-4 equation, introducing hyperbolic, trigonometric, and rational function solutions. The method is shown to be influential across various fields of physics, and the control on randomness input is studied for stability in stochastic processes.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Nesrin Guler et al.
Summary: This paper discusses the comparison problem of predictors in linear mixed models by establishing equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors. The research uses matrix rank and inertia method, and extends the results to seemingly unrelated regression models.
APPLICATIONS OF MATHEMATICS
(2022)
Article
Statistics & Probability
Nesrin Guler et al.
Summary: In this study, an extended general linear model with new observations was considered without any restrictions on correlation of random vectors and rank assumptions. Various equalities and inequalities were derived for comparing the covariance matrices of BLUP of new observations with other unbiased predictors' covariance matrices using rank and inertia formulas. Additionally, the general linear mixed model was investigated under the assumption of correlated random effects and random errors, with connections between the general linear mixed model and the extended general linear model established to provide equalities and inequalities for comparing covariance matrices of BLUP of linear functions of fixed and random effects with covariance matrices of other unbiased predictors, including special cases and linear functions of partial fixed and random effects.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2021)
Article
Engineering, Electrical & Electronic
Farshid Mirzaee et al.
Summary: In this work, the nonlinear one-dimensional stochastic Sine-Gordon equation with appropriate initial and boundary conditions is considered, and a numerical scheme based on radial basis functions (RBFs) and finite difference method is presented for providing the approximate solution. The time variable is overcome and the unknown function is estimated using strictly positive definite RBFs, such as Gaussian, in time step n. Several examples are given to verify the accuracy and efficiency of the provided solution.
INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS
(2021)
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Computer Science, Interdisciplinary Applications
Farshid Mirzaee et al.
ENGINEERING WITH COMPUTERS
(2020)
Article
Statistics & Probability
Yongge Tian et al.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2020)
Article
Statistics & Probability
Hong Jiang et al.
STATISTICS & PROBABILITY LETTERS
(2020)
Article
Multidisciplinary Sciences
Nesrin Guler et al.
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
(2019)
Article
Statistics & Probability
Changli Lu et al.
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Statistics & Probability
Changli Lu et al.
Article
Statistics & Probability
Y. Tian
STATISTICAL PAPERS
(2017)
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Yongge Tian et al.
STATISTICAL METHODS AND APPLICATIONS
(2016)
Article
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Changli Lu et al.
STATISTICS & PROBABILITY LETTERS
(2015)
Correction
Statistics & Probability
Xingwei Ren
STATISTICS & PROBABILITY LETTERS
(2015)
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Statistics & Probability
Hu Yang et al.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2014)
Article
Statistics & Probability
Baomin Dong et al.
JOURNAL OF MULTIVARIATE ANALYSIS
(2014)
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Statistics & Probability
Yongge Tian
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
(2013)
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Mathematics, Applied
Yongge Tian
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2012)
Article
Mathematics, Applied
Yongge Tian
LINEAR ALGEBRA AND ITS APPLICATIONS
(2010)
Article
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Jianwen Xu et al.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2007)
Article
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H Haupt et al.
JOURNAL OF MULTIVARIATE ANALYSIS
(2005)
