Abstract
This chapter presents the basic concepts and results of the theory of testing statistical hypotheses. The generalized likelihood ratio tests that are discussed can be applied to testing in the presence of nuisance parameters. Besides the likelihood ratio tests, for testing in the presence of nuisance parameters one can use conditional tests. The chapter also presents the motivation for steps of the proof of the randomization principle theorem. It considers the case of a single observation, but the extension to the case of n observations will be obvious. The chapter presents an approach that requires unbiasedness and explains how the theory of testing statistical hypotheses is related to the theory of confidence intervals. It reviews the major testing procedures for parameters of normal distributions and is intended as a convenient reference for users rather than an exposition of new concepts or results.
Keywords
Statistical hypothesis testingExtension (predicate logic)Nuisance parameterMathematicsEconometricsExposition (narrative)Statistical theoryComputer scienceStatistics
Related Publications
Design and Analysis in Dissemination and Implementation Research
There remains a lack of consensus on methodological approaches to the study of dissemination and implementation (D&I) processes, and especially tests of implementation strategie...
Maximum Likelihood Estimation in Truncated Samples
In this paper we consider the problem of estimation of parameters from a sample in which only the first $r$ (of $n$) ordered observations are known. If $r = \\lbrack qn \\rbrack...
Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses
In this paper, we develop a classical approach to model selection. Using the Kullback-Leibler Information Criterion to measure the closeness of a model to the truth, we propose ...
The Simes Method for Multiple Hypothesis Testing With Positively Dependent Test Statistics
Abstract The Simes method for testing intersection of more than two hypotheses is known to control the probability of type I error only when the underlying test statistics are i...
Mean and Covariance Structures (MACS) Analyses of Cross-Cultural Data: Practical and Theoretical Issues
Practical and theoretical issues are discussed for testing (a) the comparability, or measurement equivalence, of psychological constructs and (b) detecting possible sociocultura...
Publication Info
- Year
- 2021
- Type
- other
- Pages
- 373-428
- Citations
- 5220
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
5220
OpenAlex
Cite This
E. L. Lehmann
(2021).
Testing Statistical Hypotheses.
Wiley series in probability and statistics
, 373-428.
https://doi.org/10.1002/9781119243830.ch12
Identifiers
- DOI
- 10.1002/9781119243830.ch12