674 research outputs found
Lower Bounds for Heights in Relative Galois Extensions
The goal of this paper is to obtain lower bounds on the height of an
algebraic number in a relative setting, extending previous work of Amoroso and
Masser. Specifically, in our first theorem we obtain an effective bound for the
height of an algebraic number when the base field is a
number field and is Galois. Our second result
establishes an explicit height bound for any non-zero element which is
not a root of unity in a Galois extension , depending on
the degree of and the number of conjugates of
which are multiplicatively independent over . As a consequence, we
obtain a height bound for such that is independent of the
multiplicative independence condition
Heteroskedasticity testing through a comparison of Wald statistics
This paper shows that a test for heteroskedasticity within the context of classical linear regression can be based on the difference between Wald statistics in heteroskedasticity-robust and nonrobust forms. The test is asymptotically distributed under the null hypothesis of homoskedasticity as chi-squared with one degree of freedom. The power of the test is sensitive to the choice of parametric restriction used by the Wald statistics, so the supremum of a range of individual test statistics is proposed. Two versions of a supremum-based test are considered: the first version does not have a known asymptotic null distribution, so the bootstrap is employed to approximate its empirical distribution. The second version has a known asymptotic distribution and, in some cases, is asymptotically pivotal under the null. A simulation study illustrates the use and finite-sample performance of both versions of the test. In this study, the bootstrap is found to provide better size control than asymptotic critical values, namely with heavy-tailed, asymmetric distributions of the covariates. In addition, the use of well-known modifications of the heteroskedasticity consistent covariance matrix estimator of OLS coefficients is also found to benefit the tests’ overall behaviour.info:eu-repo/semantics/publishedVersio
Margins, Gravity, and Causality: Export Diversification and Income Levels Reconsidered
The Shadow Economy in International Comparison: Options for Economic Policy Derived from an OECD Panel Analysis
Functional and patient-reported outcomes of the swanson metacarpo-phalangeal arthroplasty in the rheumatoid hand
STAR-GARCH Models for Stock Market Interactions in the Pacific Basin Region, Japan and US
Does taking the shadow economy into account matter when measuring aggregate efficiency?
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