Evaluation of the Goldfeld-Quandt test and alternatives (original) (raw)

W, LR and LM Tests in the Formation of the Preliminary Test Estimator

2006

summary This paper deflnes the preliminary test estimator (PTE) of the univariate normal mean under the original as well as the Edgeworth size corrected Wald (W), likelihood ratio (LR) and Lagrange multiplier (LM) tests. The bias and mean squared error (MSE) functions of the estimators are derived. The con∞icts among the biases and the MSEs of the PTEs under the three original and the size corrected tests have been obtained. It is found that instead of the original W, LR and LM tests, the use of the Edgeworth size corrected W, LR and LM tests in the formation of the PTEs reduces the con∞ict among the biases and MSEs of the estimators remarkably.

Ewp 0402 Issn 1485-6441 Testing for Normality in the Linear Regression Model : An Empirical Likelihood Ratio Test

2004

Author Contact: Lauren Dong, Statistics Canada; e-mail: Lauren.Dong@statcan.can; FAX: (613) 951-3292 David Giles*, Dept. of Economics, University of Victoria, P.O. Box 1700, STN CSC, Victoria, B.C., Canada V8W 2Y2; e-mail: dgiles@uvic.ca; FAX: (250) 721-6214 * Corresponding co-author Abstract The empirical likelihood ratio (ELR) test for the problem of testing for normality in a linear regression model is derived in this paper. The sampling properties of the ELR test and four other commonly used tests are explored and analyzed using Monte Carlo simulation. The ELR test has good power properties against various alternative hypotheses.

Preliminary test estimators for the multivariate normal mean based on the modified W, LR and LM tests

2003

In this paper we consider the preliminary test estimators (PTEs) of the mean vector of multivariate normal distribution under the modified Wald, likelihood ratio, and Lagrange multiplier tests. The properties of the estimators have been investigated under some popular statistical criteria. It has been observed that with respect to the quadratic bias the Wald test based PTE performs better than those based on the likelihood ratio and Lagrange multiplier tests. Whereas, with respect to the quadratic risk the Lagrange multiplier test based PTE performs better than those based on the likelihood ratio and Wald tests. The results of this study reveal that the use of the three modified tests in the formation of the PTEs significantly reduces the conflict among the PTEs as compared to the estimators based on the three original tests in terms of both quadratic bias and risk properties.

Some Specification Tests for the Linear Regression Model

Sociological Methods & Research, 1992

A great deal of recent work in econometrics has focused on the development of tests to detect violations of the assumptions of ordinary least squares regression. These tests are referred to collectively as specification tests. This article evaluates some important and computationally convenient specification tests for the normal regression model as applied to cross-sectional data. Because these tests achieve their optimal properties in large samples, their size and power in finite samples are of great interest and are evaluated with Monte Carlo simulations. Although the authors' experiments showed a tendency toward overrejection in some tests, their results suggest that specific variations of the RESET and information matrix tests behave quite well even in small samples. They conclude by proposing a strategy for the sequential application of specification tests.

Estimation of Parameters of Linear Econometric Model and the Power of Test in the Presence of Heteroscedasticity Using Monte- Carlo Approach

This paper is concerned with the estimation of parameters of linear econometric model and the power of test in the presence of heteroscedasticity using Monte-Carlo approach. The Monte Carlo approach was used for the study in which random samples of sizes 20, 50 and 100, each replicated 50 times were generated. Since the linear econometric model was considered, a fixed X variable for the different sample sizes was generated to follow a uniform distribution while 50 replicates of the stochastic error term for different sample sizes followed a normal distribution. Two functional form of heteroscedasticity () () 1 2 h x X and h x X = = were introduced into the econometric model with the aim of studying the behaviour of the parameters to be estimated. 50 replicates of the dependent variable for each sample size was generated from the model () () i i Y x u h x α β = + + where the parameters, and α β were assumes to be 0.5 and 2.0 respectively. The Ordinary Least Squares (OLS) and the Generalized Least Squares (GLS) estimators were studied to identify which is more efficient in the presence of the two functional forms of heteroscedasticity considered. Both estimators were unbiased and consistent but none was convincingly more efficient than the other. The power of test was used to examine which test of heteroscedasticity (i.e., Glejser, Breusch-Pagan and White) is most efficient in the detection of any of the two forms of heteroscedasticity using different sample sizes. Glejser test detects heteroscedasticity more efficiently even in small sample sizes while White test is not as efficient when sample size is small compared to when the sample size is large.