Abstract
Asymptotic methods for testing statistical hypotheses under the general framework of Quadratic Form tests (QF test) are developed in this chapter. These include methods to derive the asymptotic null and local alternative distributions of any QF test. Several commonly used test statistics are shown to be special cases of QF tests, including Wilks’s likelihood ratio test, Wald’s test, Rao’s score test, Neyman’s \(C(\alpha )\) test, the Lagrangian multiplier test, as well as tests based on estimating equations. The concept of asymptotically efficient QF tests and Pitman’s efficiency are also introduced.
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Li, B., Babu, G.J. (2019). Asymptotic Hypothesis Test. In: A Graduate Course on Statistical Inference. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9761-9_11
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