Distributed Optimization with Multiple Linear Equality Constraints and Convex Inequality Constraints

2019 ◽  
Author(s):  
Wen-Ting Lin ◽  
Yan-Wu Wang ◽  
Jiang-Wen Xiao
Keyword(s):  
Distributed Optimization ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Linear Equality Constraints ◽  
Linear Equality ◽  
Convex Inequality

Linear Equality Constraints in the General Linear Mixed Model

Biometrics ◽  
2001 ◽  
Vol 57 (4) ◽  
pp. 1185-1190 ◽  
Author(s):  
Lloyd J. Edwards ◽  
Paul W. Stewart ◽  
Keith E. Muller ◽  
Ronald W. Helms
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Equality Constraints ◽  
General Linear ◽  
Linear Equality Constraints ◽  
Linear Equality ◽  
General Linear Mixed Model

UNIFORM INFERENCE IN A GENERALIZED INTERVAL ARITHMETIC CENTER AND RANGE LINEAR MODEL

2021 ◽  
pp. 1-43
Author(s):  
Yanqin Fan ◽  
Xuetao Shi
Keyword(s):  
Interval Arithmetic ◽  
Inequality Constraints ◽  
Coefficient Of Determination ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Linear Inequality Constraints ◽  
Linear Equality Constraints ◽  
Linear Equality ◽  
Random Intervals ◽  
Interval Valued

Via generalized interval arithmetic, we propose a Generalized Interval Arithmetic Center and Range (GIA-CR) model for random intervals, where parameters in the model satisfy linear inequality constraints. We construct a constrained estimator of the parameter vector and develop asymptotically uniformly valid tests for linear equality constraints on the parameters in the model. We conduct a simulation study to examine the finite sample performance of our estimator and tests. Furthermore, we propose a coefficient of determination for the GIA-CR model. As a separate contribution, we establish the asymptotic distribution of the constrained estimator in Blanco-Fernández (2015, Multiple Set Arithmetic-Based Linear Regression Models for Interval-Valued Variables) in which the parameters satisfy an increasing number of random inequality constraints.

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