Testing inequality constraints in a linear regression model with spherically symmetric disturbances

Zhu, Rong; Zhou, Sherry

doi:10.1007/s11424-014-1150-0

Cited by 2 publications

(2 citation statements)

References 28 publications

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“…[60] gives conservative likelihood ratio test using data-dependent degree of freedom. [76] gives Wald test under inequality constraint in linear model with spherically symmetric disturbance. [43] proposes an extended MaxT test and gets the power improvement.…”

Section: Related Workmentioning

confidence: 99%

Constrained High Dimensional Statistical Inference

Yu,

Gupta,

Kolar

2019

Preprint

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In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained. However, in many problems, there are natural constraints on model parameters and one is interested in whether the parameters are on the boundary of the constraint or not. e.g. non-negativity constraints for transmission rates in network diffusion. In this paper, we provide algorithms to solve this problem of hypothesis testing in high-dimensional statistical models under constrained parameter space. We show that following our testing procedure we are able to get asymptotic designed Type I error under the null. Numerical experiments demonstrate that our algorithm has greater power than the standard algorithms where the constraints are ignored. We demonstrate the effectiveness of our algorithms on two real datasets where we have intrinsic constraints on the parameters.

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Section: Related Workmentioning

confidence: 99%

Constrained High Dimensional Statistical Inference

Yu,

Gupta,

Kolar

2019

Preprint

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“…When the preliminary information represented by the restrictions is uncertain, investigators often implement a pre-test to examine the validity of the restrictions. A great deal of research has been done on testing under inequality restrictions for linear models such as Wolak (1987Wolak ( , 1989, Gourieroux et al (1982), Geng and Wan (2000), Fonseca et al (2015) and Zhu and Zhou (2014). This paper focuses on Bayesian methods whose estimation procedure uses the information obtained from observations and historical data or other sources.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation Approach for Linear Regression Models with Linear Inequality Restrictions

Seifollahi¹,

Kamary²,

Bevrani³

2021

Preprint

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Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological knowledge and motivated by machine learning applications of high-consequence engineering systems (Agrell, 2019;Veiga and Marrel, 2012). Some studies on the multiple linear models consider known linear combinations of the regression coefficient parameters restricted between upper and lower bounds. In the present paper, we consider both univariate and multivariate general linear models subjected to this kind of linear restrictions. So far, research on univariate cases based on Bayesian methods is all under the condition that the coefficient matrix of the linear restrictions is a square matrix of full rank. This condition is not, however, always feasible. Another difficulty arises at the estimation step by implementing the Gibbs algorithm, which exhibits, in most cases, slow convergence. This paper presents a Bayesian method to estimate the regression parameters when the matrix of the constraints providing the set of linear inequality restrictions undergoes no condition. For the multivariate case, our Bayesian method estimates the regression parameters when the number of the constrains is less than the number of the regression coefficients in each multiple linear models. We examine the efficiency of our Bayesian method through simulation studies for both univariate and multivariate regressions. After that, we illustrate that the convergence of our algorithm is relatively faster than the previous methods. Finally, we use our approach to analyze two real datasets.

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Testing inequality constraints in a linear regression model with spherically symmetric disturbances

Cited by 2 publications

References 28 publications

Constrained High Dimensional Statistical Inference

Constrained High Dimensional Statistical Inference

Bayesian Estimation Approach for Linear Regression Models with Linear Inequality Restrictions

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