Conditional Properties of Statistical Procedures

Robinson, Gwen

doi:10.1214/aos/1176344725

Cited by 81 publications

(62 citation statements)

References 26 publications

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“…A more successful methodology, perhaps because of its simplicity, is estimation of indicator functions, detailed in Section 4. This methodology is mainly due to Berger (1985a), but had some seeds in Kiefer (1977) andRobinson (1979a). In Section 5, we discuss generalisations of this methodology, which might be called estimation of accuracy.…”

Section: IImentioning

confidence: 99%

Frequentist Post-Data Inference

Goutis¹,

Casella²

1995

International Statistical Review / Revue Internationale de Stat

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SummaryThe end result of an experiment is an inference, which is typically made after the data have been seen (a post-data inference). Classical frequency theory has evolved around pre-data inferences, those that can be made in the planning stages of an experiment, before data are collected. Such pre-data inferences are often not reasonable as post-data inferences, leaving a frequentist with no inference conditional on the observed data. We review the various methodologies that have been suggested for frequentist post-data inference, and show how recent results have given us a very reasonable methodology. We also discuss how the pre-data/post-data distinction fits in with, and subsumes, the Bayesian/frequentist distinction.

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Section: IImentioning

confidence: 99%

Frequentist Post-Data Inference

Goutis¹,

Casella²

1995

International Statistical Review / Revue Internationale de Stat

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“…Such an approach yields a 0-1 answer, rules that are often criticised as being data insensitive. Once a partition of the sample space into two regions has been decided, all values of data in the acceptance region are considered to cast the same evidence for H 0 whereas all data in the rejection region bring the same evidence against H 0 • This binary behaviour has been considered as a serious drawback from theoretical point of view (e. g. DeGroot 1973, Berger 1985, Kiefer 1977, Robinson 1979. Several authors have proposed alternative approaches to the problem including the use of Bayesian posterior probabilities (DeGroot 1973), the report of conditional confidence (Kiefer 1977) and a decision theoretical approach to the estimation of accuracy of testing (Hwang et al 1992).…”

Section: Introductionmentioning

confidence: 99%

Assessing Evidence in Multiple Hypotheses

Goutis

Casella

Wells

1996

Journal of the American Statistical Association

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SummaryWe formulate the problem of choosing between two hypotheses as a problem of constructing a data-dependent evidential measure for or against the null hypothesis.Such a measure should obey some intuitive desiderata which we state as axioms. We examine critically the behaviour of common rules of assessing evidence in higher dimensions, such as combinations of p-values and Bayes posterior probabilities, and clarify the connection between hypothesis testing and our approach. Decision theoretical tools are also used to evaluate various rules and a general admissibility result is provided. A discussion comparing different methods of assessing evidence is included.

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“…It wasn't until 20 years later, however, that the theory was suitably formalized to allow for relatively easy evaluations of conditional properties. Robinson (1979aRobinson ( , 1979b explicitly formalized the theory with definitions on the types of bets and the biases involved. His formulation is much more general but can be used to evaluate a procedures conditional properties.…”

Section: Conditional Propertiesmentioning

confidence: 99%

“…See Bondar (1977), Robinson (1979a,1979b), or Casella (1988 for a more extensive discussion of these ideas.…”

Section: Pb(b E C(x)jx E A) S1-a-t Y Bmentioning

confidence: 99%

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Developments in Decision-Theoretic Variance Estimation

Maatta¹,

Casella²

1990

Statist. Sci.

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This article traces the history of the problem of estimating the variance, 0" 2 , based on a random sample from a normal distribution with mean J-l unknown. Considered are both the point estimation and confidence interval cases. We see that improvement over both usual estimators follows a remarkably parallel development and stemmed from the innovative ideas presented in Stein (1964). We examine developments through the most recent dealing with improved confidence intervals and conditional evaluations of interval estimators.-2-

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Conditional Properties of Statistical Procedures

Cited by 81 publications

References 26 publications

Frequentist Post-Data Inference

Frequentist Post-Data Inference

Assessing Evidence in Multiple Hypotheses

Developments in Decision-Theoretic Variance Estimation

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