A simulation-based evidence on the improved performance of a new modified leverage adjusted heteroskedastic consistent covariance matrix estimator in the linear regression model

Nuzhat Aftab, Sohail Chand


In this paper, we present a new heteroskedastic consistent (HC) covariance matrix estimator which considers the effect of leverage observations and which has a better approximation of its true asymptotic distribution. We point out that the basic motivation behind this new modified HC estimator is to provide an estimator which does not require any user specified values.
In terms of bias and mean squared error (MSE), a Monte Carlo simulation study provided evidence that this new estimator has better small sample properties over some existing estimators. A real-life example also evaluated the finite sample behavior in comparison to those existing estimators.


Linear Regression; Heteroskedasticity; HCs; High Leverage points; Quasi-t test

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Al-Humoud, J. & Al-Ghusain, I. (2003). Household demand

for water: A case study in kuwait. Kuwait Journal of Science and

Engineering, 30(1): 197–212.

Chatterjee, S. & Hadi, A.S. (2015). Regression analysis by

example. John Wiley & Sons, NJ, USA. pp 144 .

Cribari-Neto, F. (2004). Asymptotic inference under

heteroskedasticity of unknown form. Computational Statistics &

Data Analysis, 45(2): 215–233.

Cribari-Neto, F. & Da Silva, W. (2011). A new heteroskedasticityconsistent

covariance matrix estimator for the linear regression

model. AStA Advances in Statistical Analysis, 95(2): 129–146.

Cribari-Neto, F., Ferrari, S., & Oliveira, W.

(2005). Numerical evaluation of tests based on

different heteroskedasticity-consistent covariance matrix

estimators. Journal of Statistical Computation and Simulation,

(8): 611–628.

Cribari-Neto, F. & Galvão, N. (2003). A class of improved

heteroskedasticity-consistent covariance matrix estimators.

Communications in Statistics-Theory and Methods, 32(10): 1951–1980.

Cribari-Neto, F., Souza, T., & Vasconcellos, K. (2007). Inference

under heteroskedasticity and leveraged data. Communications in

Statistics-Theory and Methods, 36(10): 1877–1888.

Cribari-Neto, F. & Zarkos, S. (1999). Bootstrap methods for

heteroskedastic regression models: evidence on estimation and

testing. Econometric Reviews, 18(2): 211–228.

Cribari-Neto, F. and Zarkos, S. (2001). Heteroskedasticity

consistent covariance matrix estimation: White’s estimator and

the bootstrap. Journal of Statistical Computation and Simulation,

(4): 391–411.

Cribari-Neto, F. & Zarkos, S. G. (2004). Leverage-adjusted

heteroskedastic bootstrap methods. Journal of Statistical

Computation and Simulation, 74(3): 215–232.

Davidson, R. & MacKinnon, J. (1993). Estimation and inference

in econometrics. Oxford University Press, USA. pp 631.

Eicker, F. (1963). Asymptotic normality and consistency of the

least squares estimators for families of linear regressions. The

Annals of Mathematical Statistics, 34(2): 447–456.

Hausman, J. & Palmer, C. (2012). Heteroskedasticity-robust

inference in finite samples. Economics Letters, 116(2): 232–235.

Hodoshima, J. & Ando, M. (2006). The effect of non-independence

of explanatory variables and error term and heteroskedasticity

in stochastic regression models. Communications in Statistics-

Simulation and Computation, 35(2): 361–405.

Liu, R. (1988). Bootstrap procedures under some non-iid models.

The Annals of Statistics,

(4): 1696–1708.

Long, J. & Ervin, L. (2000). Using heteroscedasticity consistent

standard errors in the linear regression model. The American

Statistician, 54(3): 217–224.

MacKinnon, J. & White, H. (1985). Some heteroskedasticityconsistent

covariance matrix estimators with improved finite

sample properties. Journal of Econometrics, 29(3): 305–325.

Montgomery, D., Peck, E., Vining, G., & Vining, J. (2001).

Introduction to linear regression analysis, Volume 3. Wiley: NJ,

USA. p207.

R Development Core Team (2011). R: A Language and

Environment for Statistical Computing. RFoundation for Statistical

Computing, Vienna, Austria.

White, H. (1980). A heteroskedasticity-consistent covariance matrix

estimator and a direct test for heteroskedasticity. Econometrica.

Journal of the Econometric Society, 48(4): 817–838.


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