scholarly journals The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors

2021 ◽  
Author(s):  
Leo Michelis
Keyword(s):  
Monte Carlo ◽  
Alternative Model ◽  
Regression Models ◽  
Population Distribution ◽  
Nuisance Parameter ◽  
Linear Regression Models ◽  
Null Distributions ◽  
Finite Samples ◽  
The Monte Carlo Method ◽  
Asymptotic Expressions

This paper examines the asymptotic null distributions of the <em>J</em> and Cox non-nested tests in the framework of two linear regression models with nearly orthogonal non-nested regressors. The analysis is based on the concept of near population orthogonality (NPO), according to which the non-nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn. New distributional results emerge under NPO. The <em>J</em> and Cox tests tend to two different random variables asymptotically, each of which is expressible as a function of a nuisance parameter, <em>c</em>, a N(0,1) variate and a <em>χ</em>2(<em>q</em>) variate, where <em>q</em> is the number of non-nested regressors in the alternative model. The Monte Carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under NPO by plugging consistent estimates of <em>c</em> into the relevant asymptotic expressions. An empirical example illustrates the ‘plug in’ procedure.

scholarly journals The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors

2021 ◽  
Author(s):  
Leo Michelis
Keyword(s):  
Monte Carlo ◽  
Alternative Model ◽  
Regression Models ◽  
Population Distribution ◽  
Nuisance Parameter ◽  
Linear Regression Models ◽  
Null Distributions ◽  
Finite Samples ◽  
The Monte Carlo Method ◽  
Asymptotic Expressions

This paper examines the asymptotic null distributions of the <em>J</em> and Cox non-nested tests in the framework of two linear regression models with nearly orthogonal non-nested regressors. The analysis is based on the concept of near population orthogonality (NPO), according to which the non-nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn. New distributional results emerge under NPO. The <em>J</em> and Cox tests tend to two different random variables asymptotically, each of which is expressible as a function of a nuisance parameter, <em>c</em>, a N(0,1) variate and a <em>χ</em>2(<em>q</em>) variate, where <em>q</em> is the number of non-nested regressors in the alternative model. The Monte Carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under NPO by plugging consistent estimates of <em>c</em> into the relevant asymptotic expressions. An empirical example illustrates the ‘plug in’ procedure.

scholarly journals Homoscedasticity: an overlooked critical assumption for linear regression

2019 ◽  
Vol 32 (5) ◽  
pp. e100148
Author(s):  
Kun Yang ◽  
Justin Tu ◽  
Tian Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Regression ◽  
Regression Models ◽  
Data Distribution ◽  
The Other ◽  
Simulation Studies ◽  
Linear Regression Models ◽  
Popular Belief

Linear regression is widely used in biomedical and psychosocial research. A critical assumption that is often overlooked is homoscedasticity. Unlike normality, the other assumption on data distribution, homoscedasticity is often taken for granted when fitting linear regression models. However, contrary to popular belief, this assumption actually has a bigger impact on validity of linear regression results than normality. In this report, we use Monte Carlo simulation studies to investigate and compare their effects on validity of inference.

Accounting for Endogeneity in Regression Models Using Copulas: A Step-by-Step Guide for Empirical Studies

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alecos Papadopoulos
Keyword(s):  
Regression Models ◽  
Empirical Studies ◽  
Gaussian Copula ◽  
Supplementary File ◽  
Linear Regression Models ◽  
Finite Samples ◽  
Endogenous Regressors ◽  
Proposed Model ◽  
Present Simulation ◽  
Detailed Presentation

Abstract We provide a detailed presentation and guide for the use of Copulas in order to account for endogeneity in linear regression models without the need for instrumental variables. We start by developing the model from first principles of likelihood inference, and then focus on the Gaussian Copula. We discuss its merits and propose diagnostics to assess its validity. We analyze in detail and provide solutions to the various issues that may arise in empirical applications for applying the method. We treat the cases of both continuous and discrete endogenous regressors. We present simulation evidence for the performance of the proposed model in finite samples, and we illustrate its application by a short empirical study. A Supplementary File contains additional simulations and another empirical illustration.

scholarly journals SHRINKAGE ESTIMATION OF REGRESSION MODELS WITH MULTIPLE STRUCTURAL CHANGES

2015 ◽  
Vol 32 (6) ◽  
pp. 1376-1433 ◽  
Author(s):  
Junhui Qian ◽  
Liangjun Su
Keyword(s):  
Regression Models ◽  
Structural Changes ◽  
Equity Premium ◽  
Asymptotic Distributions ◽  
Regression Coefficients ◽  
Tuning Parameter ◽  
Linear Regression Models ◽  
Predictive Regression ◽  
Finite Samples ◽  
Fundamental Information

In this paper, we consider the problem of determining the number of structural changes in multiple linear regression models via group fused Lasso. We show that with probability tending to one, our method can correctly determine the unknown number of breaks, and the estimated break dates are sufficiently close to the true break dates. We obtain estimates of the regression coefficients via post Lasso and establish the asymptotic distributions of the estimates of both break ratios and regression coefficients. We also propose and validate a data-driven method to determine the tuning parameter. Monte Carlo simulations demonstrate that the proposed method works well in finite samples. We illustrate the use of our method with a predictive regression of the equity premium on fundamental information.

scholarly journals Impact of landmark identification and standard measurement error on cephalometric analysis using a mathematical simulation model

2012 ◽  
Vol 53 (3) ◽  
pp. 1-5
Author(s):  
Eduardo Luiz Delamare ◽  
Gabriela Salatino Liedke ◽  
Mariana Boessio Vizzotto ◽  
Heraldo Luis Dias Da Silveira ◽  
Dalva Maria Pereira Padilha ◽  
...  
Keyword(s):  
Measurement Error ◽  
Simulation Model ◽  
Mathematical Simulation ◽  
Measurement Errors ◽  
Regression Models ◽  
Linear Regression Models ◽  
Standard Measurement ◽  
Landmark Identification ◽  
The Monte Carlo Method ◽  
Impact Coefficient

Objective: To assess, using a mathematical simulation model, the participation of each coordinate involved in the formation of cephalometric angles and to determine the extent to which errors in the identification of cephalometric landmarks can, individually and collectively, influence the measurement of these angles. Material and Methods: The reference values and standard errors of 13 landmarks obtained from the analysis of 30 cephalograms were used. For each landmark, 1000 observations were simulated using the Monte Carlo method. On the basis of linear regression models, equations designed to estimate measurement errors due to landmark identification errors were obtained and analysed. Results: The coordinates most involved in the formation of the angles SNA, SNB, ANB, FMA, PPL, DFC, and AEF were Ny, Ny, Ax, Goy, Poy, Poy, and Ptmx, respectively, and the standard measurement errors for these angles were 1.2, 0.9, 0.8, 1.6, 1.5, 1.5, and 1.4, respectively. Conclusion: The standard measurement error of the angle depends on the geometric impact coefficient and the standard error of the coordinates involved in the formation of the angles, and the geometric impact coefficient varies according to the angle analysed.

scholarly journals empirical likelihood ratio based comparative study on tests for normality of residuals in linear models

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Chioneso Marange ◽  
Yongsong Qin
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Regression Models ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Simple Linear Regression ◽  
Linear Regression Models

The application of goodness-of-fit (GoF) tests in linear regression modeling is a common practice in applied statistical sciences. For instance, in simple linear regression the assumption of normality of residuals is always necessary to test before making any further inferences. The growing popularity of the use of powerful and efficient empirical likelihood ratio (ELR) based GoF tests in checking for departures from normality in various continuous distributions can be of great use in checking for distributional assumptions of residuals in linear models. Motivated by the attractive properties of the ELR based GoF tests the researchers conducted an extensive Type I error rate assessment as well as a Monte Carlo power comparison of selected ELR GoF tests with well-known existing tests against symmetric and asymmetric alternative OLS and BLUS residuals. Under the simulated scenarios, all the studied tests have good control of Type I error rates. The Monte Carlo experiments revealed the superiority of the ELR GoF tests under certain alternatives of both the OLS and BLUS residuals. Our findings also demonstrated the superiority of OLS over BLUS residuals when one is testing for normality in simple linear regression models. A real data study further revealed the applicability of the ELR based GoF tests in testing normality of residuals in linear regression models.

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