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Critères d'évaluation de la validité des estimateurs d'intervalle de confiance

Abstract : INTRODUCTION: the interpretation of confidence intervals and hypothesis tests is usually directional, drawing a distinction between superiority and inferiority. On another note, numerous statistical tools are conditional to statistics that are actually variable such as the model matrix of a generalized linear model or sample size. The aim of this thesis is to propose methods for the assessment of statistical estimators that are consistent with the use that will be done of these tools. METHODS: the consequences of ignoring the directional interpretation in the assessment of statistical tools, especially for survival analysis, were evaluated from reviews of the literature and theoretical considerations. Assessment criteria Assessment criteria based on local averages were proposed to free the assessment of statistical tools from conditioning on variable statistics, such as sample size even when such tools are conditional. Underestimation and overestimation risks were differentiated in the assessment of coverage flaws of confidence intervals. Usual estimators were reassessed with these new criteria : binomial proportion and Poisson regression estimators. RESULTS: the directional interpretation of hypothesis tests about differences in survival curves can lead to a risk of concluding in the opposite direction to the actual difference approaching 50% in some cases. New assessment criteria, in particular, one-sided local average type I error rates, showed the better behavior of the likelihood ratio test and confidence intervals compared to Rao’s score and Wald’s methods for logistic and Poisson regressions. Strictly conservative methods are relevant in some very specific contexts ; otherwise, methods based on mid-P-values should be preferred. Confidence intervals aiming at an imbalance between risks of overestimation and underestimation in order to shorten their overall width lose directional interpretation properties. CONCLUSION: the directional interpretation of hypothesis tests and confidence interval estimators should be taken into account in their design and assessment.
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Submitted on : Friday, September 24, 2021 - 3:01:13 PM
Last modification on : Wednesday, October 20, 2021 - 12:25:09 AM

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  • HAL Id : tel-03353978, version 1

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André Gillibert. Critères d'évaluation de la validité des estimateurs d'intervalle de confiance. Théorie [stat.TH]. Université Paris-Saclay, 2021. Français. ⟨NNT : 2021UPASR012⟩. ⟨tel-03353978⟩

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