Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters
| Autor: | Alexandre G. Patriota, David R. Bickel |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Engineering ranking function Operations research surprise measure Self consistent possibility theory 01 natural sciences 010104 statistics & probability $p$-value function restricted parameter space 0101 mathematics Deductive closure Possibility theory INFERÊNCIA ESTATÍSTICA deductive closure business.industry Management science 010102 general mathematics Foundation (engineering) deductive cogency empty confidence set bounded parameter ranking theory Christian ministry business |
| Zdroj: | Bernoulli 25, no. 1 (2019), 47-74 Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | Frequentist methods, without the coherence guarantees of fully Bayesian methods, are known to yield self-contradictory inferences in certain settings. The framework introduced in this paper provides a simple adjustment to $p$ values and confidence sets to ensure the mutual consistency of all inferences without sacrificing frequentist validity. Based on a definition of the compatibility of a composite hypothesis with the observed data given any parameter restriction and on the requirement of self-consistency, the adjustment leads to the possibility and necessity measures of possibility theory rather than to the posterior probability distributions of Bayesian and fiducial inference. |
| Databáze: | OpenAIRE |
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