Abstract:
It is well-known that use of ordinary least squares for estimation of linear regression
model with heteroscedastic errors, always results into inefficient estimates of the
parameters. Additionally, the consequence that attracts the serious attention of the
researchers is the inconsistency of the usual covariance matrix estimator that, in turn,
results in inaccurate inferences. The test statistics based on such covariance estimates
are usually too liberal i.e., they tend to over-reject the true null hypothesis. To
overcome such size distortion, White (1980) proposes a heteroscedasticity consistent
covariance matrix estimator (HCCME) that is known as HC0 in literature. Then
MacKinnon and White (1985) improve this estimator for small samples by presenting
three more variants, HC1, HC2 and HC3. Additionally, in the presence of influential
observations, Cribari-Neto (2004) presents HC4. An extensive available literature
advocates the use of HCCME when the problem of heteroscedasticity of unknown
from is faced. Parallel to HCCME, the use of bootstrap estimator, namely wild
bootstrap estimator is also common to improve the inferences in the presence of
heteroscedasticity of unknown form.
The present work addresses the same issue of inference for linear heteroscedastic
models using a class of improved consistent covariance estimators, including
nonparametric and bootstrap estimators. To draw improved inference, we propose
adaptive
nonparametric
versions
of
HCCME,
bias-corrected
versions
of
nonparametric HCCME, adaptive wild bootstrap estimators and weighted version of
HCCME using some adaptive estimator, already available in literature, namely,
proposed by Carroll (1982). The performance of all the estimators is evaluated by
bias, mean square error (MSE), null rejection rate (NRR) and power of test after
conducting extensive Monte Carlo simulations.
