The Experts below are selected from a list of 4443 Experts worldwide ranked by ideXlab platform
Peter M Bentler - One of the best experts on this subject based on the ideXlab platform.
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ensuring positiveness of the scaled difference chi square test statistic
Psychometrika, 2010Co-Authors: Albert Satorra, Peter M BentlerAbstract:A scaled difference test statistic [Formula: see text] that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (2001). The statistic [Formula: see text] is asymptotically equivalent to the scaled difference test statistic T(d) introduced in Satorra (2000), which requires more involved computations beyond standard output of SEM software. The test statistic [Formula: see text] has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the Implicit Function Theorem, this note develops an improved scaling correction leading to a new scaled difference statistic T(d) that avoids negative chi-square values.
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ensuring positiveness of the scaled difference chi square test statistic
Department of Statistics UCLA, 2008Co-Authors: Albert Satorra, Peter M BentlerAbstract:A scaled difference test statistic T_tildad that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (2001). The statistic T_tildad is asymptotically equivalent to the scaled difference test statistic T_hatd introduced in Satorra (2000), which requires more involved computations beyond standard output of SEM software. The test statistic T_tildad has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the Implicit Function Theorem, this note develops an improved scaling correction leading to a new scaled difference statistic T_hatd that avoids negative chi-square values.
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ensuring positiveness of the scaled difference chi square test statistic escholarship
2008Co-Authors: Albert Satorra, Peter M BentlerAbstract:A scaled difference test statistic T_tildad that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (2001). The statistic T_tildad is asymptotically equivalent to the scaled difference test statistic T_hatd introduced in Satorra (2000), which requires more involved computations beyond standard output of SEM software. The test statistic T_tildad has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the Implicit Function Theorem, this note develops an improved scaling correction leading to a new scaled difference statistic T_hatd that avoids negative chi-square values.
Albert Satorra - One of the best experts on this subject based on the ideXlab platform.
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ensuring positiveness of the scaled difference chi square test statistic
Psychometrika, 2010Co-Authors: Albert Satorra, Peter M BentlerAbstract:A scaled difference test statistic [Formula: see text] that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (2001). The statistic [Formula: see text] is asymptotically equivalent to the scaled difference test statistic T(d) introduced in Satorra (2000), which requires more involved computations beyond standard output of SEM software. The test statistic [Formula: see text] has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the Implicit Function Theorem, this note develops an improved scaling correction leading to a new scaled difference statistic T(d) that avoids negative chi-square values.
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ensuring positiveness of the scaled difference chi square test statistic
Department of Statistics UCLA, 2008Co-Authors: Albert Satorra, Peter M BentlerAbstract:A scaled difference test statistic T_tildad that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (2001). The statistic T_tildad is asymptotically equivalent to the scaled difference test statistic T_hatd introduced in Satorra (2000), which requires more involved computations beyond standard output of SEM software. The test statistic T_tildad has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the Implicit Function Theorem, this note develops an improved scaling correction leading to a new scaled difference statistic T_hatd that avoids negative chi-square values.
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ensuring positiveness of the scaled difference chi square test statistic escholarship
2008Co-Authors: Albert Satorra, Peter M BentlerAbstract:A scaled difference test statistic T_tildad that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (2001). The statistic T_tildad is asymptotically equivalent to the scaled difference test statistic T_hatd introduced in Satorra (2000), which requires more involved computations beyond standard output of SEM software. The test statistic T_tildad has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the Implicit Function Theorem, this note develops an improved scaling correction leading to a new scaled difference statistic T_hatd that avoids negative chi-square values.
Alexey A Tretyakov - One of the best experts on this subject based on the ideXlab platform.
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Implicit Function and tangent cone Theorems for singular inclusions and applications to nonlinear programming
Optimization Letters, 2019Co-Authors: Ewa M. Bednarczuk, Agnieszka Prusinska, Alexey A TretyakovAbstract:The paper is devoted to the Implicit Function Theorem involving singular mappings. We also discuss the form of the tangent cone to the solution set of the generalized equations in singular case and give some examples of applications to nonlinear programming and complementarity problems.
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a short elementary proof of the lagrange multiplier Theorem
Optimization Letters, 2012Co-Authors: Olga Brezhneva, Alexey A Tretyakov, Stephen E WrightAbstract:We present a short elementary proof of the Lagrange multiplier Theorem for equality-constrained optimization. Most proofs in the literature rely on advanced analysis concepts such as the Implicit Function Theorem, whereas elementary proofs tend to be long and involved. By contrast, our proof uses only basic facts from linear algebra, the definition of differentiability, the critical-point condition for unconstrained minima, and the fact that a continuous Function attains its minimum over a closed ball.
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an elementary proof of the lagrange multiplier Theorem in normed linear spaces
Optimization, 2012Co-Authors: Olga Brezhneva, Alexey A TretyakovAbstract:We present an elementary proof of the Lagrange multiplier Theorem for optimization problems with equality constraints in normed linear spaces. Most proofs in the literature rely on advanced concepts and results, such as the Implicit Function Theorem and the Lyusternik Theorem. By contrast, the proof given in this article employs only basic results from linear algebra, the critical-point condition for unconstrained minima and the fact that a continuous Function attains its minimum over a closed ball in the finite-dimensional space.
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higher order Implicit Function Theorems and degenerate nonlinear boundary value problems
Communications on Pure and Applied Analysis, 2007Co-Authors: Olga Brezhneva, Alexey A Tretyakov, Jerrold E MarsdenAbstract:The first part of this paper considers the problem of solving an equation of the form F(x,y) = 0, for y = φ(x) as a Function of x, where F : X x Y → Z is a smooth nonlinear mapping between Banach spaces. The focus is on the case in which the mapping F is degenerate at some point (x^*; y^*) with respect to y, i.e., when F' _y (x^*; y^*), the derivative of F with respect to y, is not invertible and, hence, the classical Implicit Function Theorem is not applicable. We present pth-order generalizations of the Implicit Function Theorem for this case. The second part of the paper uses these pth-order Implicit Function Theorems to derive sufficient conditions for the existence of a solution of degenerate nonlinear boundary-value problems for second-order ordinary differential equations in cases close to resonance. The last part of the paper presents a modified perturbation method for solving degenerate second-order boundary value problems with a small parameter. The results of this paper are based on the constructions of p-regularity theory, whose basic concepts and main results are given in the paper Factor-analysis of nonlinear mappings: p- regularity theory by Tret'yakov and Marsden (Communications on Pure and Applied Analysis, 2 (2003), 425-445).
Arutyunov A.v. - One of the best experts on this subject based on the ideXlab platform.
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Implicit Function Theorem without a priori assumptions about normality
'Pleiades Publishing Ltd', 2020Co-Authors: Arutyunov A.v.Abstract:The equation F(x, σ) = 0,x K, in which σ is a parameter and x is an unknown taking values in a given convex cone in a Banach space X, is considered. This equation is examined in a neighborhood of a given solution (x*, σ*) for which the Robinson regularity condition may be violated. Under the assumption that the 2-regularity condition (defined in the paper), which is much weaker than the Robinson regularity condition, is satisfied, an Implicit Function Theorem is obtained for this equation. This result is a generalization of the known Implicit Function Theorems even for the case when the cone K coincides with the entire space X. © MAIK "Nauka/Interperiodica" (Russia), 2006
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On Implicit Function Theorems at abnormal points
'Pleiades Publishing Ltd', 2020Co-Authors: Arutyunov A.v.Abstract:We consider the equation F(x, σ) = 0, x ∈ K, in which σ is a parameter and x is an unknown variable taking values in a specified convex cone K lying in a Banach space X. This equation is investigated in a neighborhood of a given solution (x*, σ*), where Robinson's constraint qualification may be violated. We introduce the 2-regularity condition, which is considerably weaker than Robinson's constraint qualification; assuming that it is satisfied, we obtain an Implicit Function Theorem for this equation. The Theorem is a generalization of the known Implicit Function Theorems even in the case when the cone K coincides with the whole space X. © 2010 Pleiades Publishing, Ltd
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Implicit Function Theorem as a realization of the lagrange principle. Abnormal points
'IOP Publishing', 2020Co-Authors: Arutyunov A.v.Abstract:A smooth non-linear map is studied in a neighbourhood of an abnormal (degenerate) point. Inverse Function and Implicit Function Theorems are proved. The proof is based on the examination of a family of constrained extremal problems; second-order necessary conditions, which make sense also in the abnormal case, are used in the process. If the point under consideration is normal, then these conditions turn into the classical ones. Bibliography: 15 titles
Asen L. Dontchev - One of the best experts on this subject based on the ideXlab platform.
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a nonsmooth robinson s inverse Function Theorem in banach spaces
Mathematical Programming, 2016Co-Authors: Radek Cibulka, Asen L. DontchevAbstract:In a recent paper, Izmailov (Math Program Ser A 147:581---590, 2014) derived an extension of Robinson's Implicit Function Theorem for nonsmooth generalized equations in finite dimensions, which reduces to Clarke's inverse Function Theorem when the generalized equation is just an equation. Pales (J Math Anal Appl 209:202---220, 1997) gave earlier a generalization of Clarke's inverse Function Theorem to Banach spaces by employing Ioffe's strict pre-derivative. In this paper we generalize both Theorems of Izmailov and Pales to nonsmooth generalized equations in Banach spaces.
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newton s method for generalized equations a sequential Implicit Function Theorem
Mathematical Programming, 2010Co-Authors: Asen L. Dontchev, R T RockafellarAbstract:In an extension of Newton’s method to generalized equations, we carry further the Implicit Function Theorem paradigm and place it in the framework of a mapping acting from the parameter and the starting point to the set of all associated sequences of Newton’s iterates as elements of a sequence space. An inverse Function version of this result shows that the strong regularity of the mapping associated with the Newton sequences is equivalent to the strong regularity of the generalized equation mapping.
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robinson s Implicit Function Theorem and its extensions
Mathematical Programming, 2008Co-Authors: Asen L. Dontchev, R T RockafellarAbstract:S. M. Robinson published in 1980 a powerful Theorem about solutions to certain “generalized equations” corresponding to parameterized variational inequalities which could represent the first-order optimality conditions in nonlinear programming, in particular. In fact, his result covered much of the classical Implicit Function Theorem, if not quite all, but went far beyond that in ideas and format. Here, Robinson’s Theorem is viewed from the perspective of more recent developments in variational analysis as well as some lesser-known results in the Implicit Function literature on equations, prior to the advent of generalized equations. Extensions are presented which fully cover such results, translating them at the same time to generalized equations broader than variational inequalities. Robinson’s notion of first-order approximations in the absence of differentiability is utilized in part, but even looser forms of approximation are shown to furnish significant information about solutions.
