A simulation-based evidence on the improved performance of a new modified leverage adjusted heteroskedastic consistent covariance matrix estimator in the linear regression model
Keywords:
Linear Regression, Heteroskedasticity, HCs, High Leverage points, Quasi-t testAbstract
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.
References
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.