224 research outputs found
Finite Sample Properties of Tests Based on Prewhitened Nonparametric Covariance Estimators
We analytically investigate size and power properties of a popular family of
procedures for testing linear restrictions on the coefficient vector in a
linear regression model with temporally dependent errors. The tests considered
are autocorrelation-corrected F-type tests based on prewhitened nonparametric
covariance estimators that possibly incorporate a data-dependent bandwidth
parameter, e.g., estimators as considered in Andrews and Monahan (1992), Newey
and West (1994), or Rho and Shao (2013). For design matrices that are generic
in a measure theoretic sense we prove that these tests either suffer from
extreme size distortions or from strong power deficiencies. Despite this
negative result we demonstrate that a simple adjustment procedure based on
artificial regressors can often resolve this problem.Comment: Some material adde
How Reliable are Bootstrap-based Heteroskedasticity Robust Tests?
We develop theoretical finite-sample results concerning the size of wild
bootstrap-based heteroskedasticity robust tests in linear regression models. In
particular, these results provide an efficient diagnostic check, which can be
used to weed out tests that are unreliable for a given testing problem in the
sense that they overreject substantially. This allows us to assess the
reliability of a large variety of wild bootstrap-based tests in an extensive
numerical study.Comment: 59 pages, 1 figur
Power in High-Dimensional Testing Problems
Fan et al. (2015) recently introduced a remarkable method for increasing
asymptotic power of tests in high-dimensional testing problems. If applicable
to a given test, their power enhancement principle leads to an improved test
that has the same asymptotic size, uniformly non-inferior asymptotic power, and
is consistent against a strictly broader range of alternatives than the
initially given test. We study under which conditions this method can be
applied and show the following: In asymptotic regimes where the dimensionality
of the parameter space is fixed as sample size increases, there often exist
tests that can not be further improved with the power enhancement principle.
However, when the dimensionality of the parameter space increases sufficiently
slowly with sample size and a marginal local asymptotic normality (LAN)
condition is satisfied, every test with asymptotic size smaller than one can be
improved with the power enhancement principle. While the marginal LAN condition
alone does not allow one to extend the latter statement to all rates at which
the dimensionality increases with sample size, we give sufficient conditions
under which this is the case.Comment: 27 page
Valid Heteroskedasticity Robust Testing
Tests based on heteroskedasticity robust standard errors are an important
technique in econometric practice. Choosing the right critical value, however,
is not simple at all: conventional critical values based on asymptotics often
lead to severe size distortions; and so do existing adjustments including the
bootstrap. To avoid these issues, we suggest to use smallest size-controlling
critical values, the generic existence of which we prove in this article for
the commonly used test statistics. Furthermore, sufficient and often also
necessary conditions for their existence are given that are easy to check.
Granted their existence, these critical values are the canonical choice: larger
critical values result in unnecessary power loss, whereas smaller critical
values lead to over-rejections under the null hypothesis, make spurious
discoveries more likely, and thus are invalid. We suggest algorithms to
numerically determine the proposed critical values and provide implementations
in accompanying software. Finally, we numerically study the behavior of the
proposed testing procedures, including their power properties.Comment: Minor changes; some references added; some minor errors correcte
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