The Experts below are selected from a list of 3594 Experts worldwide ranked by ideXlab platform

Dewi Rahardja - One of the best experts on this subject based on the ideXlab platform.

Anirban Dasgupta - One of the best experts on this subject based on the ideXlab platform.

  • confidence intervals for a Binomial Proportion and asymptotic expansions
    Annals of Statistics, 2002
    Co-Authors: Lawrence D Brown, Anirban Dasgupta
    Abstract:

    p ± zα/2n −1/2 ( ˆ p(1 −ˆ p)) 1/2 is currently in near universal use. We first show that the coverage properties of the Wald interval are persistently poor and defy virtually all conventional wisdom. We then proceed to a theoretical comparison of the standard interval and four additional alternative intervals by asymptotic expansions of their coverage probabilities and expected lengths. The four additional interval methods we study in detail are the score-test interval (Wilson), the likelihood-ratio-test interval, a Jeffreys prior Bayesian interval and an interval suggested by Agresti and Coull. The asymptotic expansions for coverage show that the first three of these alternative methods have coverages that fluctuate about the nominal value, while the Agresti– Coull interval has a somewhat larger and more nearly conservative coverage function. For the five interval methods we also investigate asymptotically their average coverage relative to distributions for p supported within (0, 1). In terms of expected length, asymptotic expansions show that the Agresti– Coull interval is always the longest of these. The remaining three are rather comparable and are shorter than the Wald interval except for p near 0 or 1. These analytical calculations support and complement the findings and the recommendations in Brown, Cai and DasGupta (Statist. Sci. (2001) 16 101–133).

  • interval estimation for a Binomial Proportion
    Statistical Science, 2001
    Co-Authors: Lawrence D Brown, Anirban Dasgupta
    Abstract:

    We revisit the problem of interval estimation of a Binomial Proportion. The erratic behavior of the coverage probability of the stan- d ardWaldconfid ence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that the chaotic coverage properties of the Waldinter- val are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects andcannot be trusted . This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and con- text. Each interval is examinedfor its coverage probability andits length. Basedon this analysis, we recommendthe Wilson interval or the equal- tailedJeffreys prior interval for small n andthe interval suggestedin Agresti andCoull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.

Chand K Midha - One of the best experts on this subject based on the ideXlab platform.

Mans Thulin - One of the best experts on this subject based on the ideXlab platform.

  • approximate bayesianity of frequentist confidence intervals for a Binomial Proportion
    The American Statistician, 2017
    Co-Authors: Mans Thulin, Rolf Larsson
    Abstract:

    ABSTRACTThe well-known Wilson and Agresti–Coull confidence intervals for a Binomial Proportion p are centered around a Bayesian estimator. Using this as a starting point, similarities between frequentist confidence intervals for Proportions and Bayesian credible intervals based on low-informative priors are studied using asymptotic expansions. A Bayesian motivation for a large class of frequentist confidence intervals is provided. It is shown that the likelihood ratio interval for p approximates a Bayesian credible interval based on Kerman’s neutral noninformative conjugate prior up to O(n− 1) in the confidence bounds. For the significance level α ≲ 0.317, the Bayesian interval based on the Jeffreys’ prior is then shown to be a compromise between the likelihood ratio and Wilson intervals. Supplementary materials for this article are available online.

  • the cost of using exact confidence intervals for a Binomial Proportion
    Electronic Journal of Statistics, 2014
    Co-Authors: Mans Thulin
    Abstract:

    When computing a confidence interval for a Binomial Proportion p one must choose between using an exact interval, which has a coverage probability of at least 1 a for all values of p, and a shorter approximate interval, which may have lower coverage for some p but that on average has coverage equal to 1 a. We investigate the cost of using the exact one and two-sided Clopper-Pearson confidence intervals rat her than shorter approximate intervals, first in terms of increased expected length and then in terms of the increase in sample size required to obtain a desired expected length. Using asymptotic expansions, we also give a closed-form formula for determining the sample size for the exact Clopper-Pearson methods. For two-sided intervals, our investigation reveals an interesting connection between the frequentist Clopper-Pearson interval and Bayesian intervals based on noninformative priors.

  • Coverage‐adjusted Confidence Intervals for a Binomial Proportion
    Scandinavian Journal of Statistics, 2013
    Co-Authors: Mans Thulin
    Abstract:

    type="main" xml:id="sjos12021-abs-0001"> We consider the classic problem of interval estimation of a Proportion p based on Binomial sampling. The ‘exact’ Clopper–Pearson confidence interval for p is known to be unnecessarily conservative. We propose coverage adjustments of the Clopper–Pearson interval that incorporate prior or posterior beliefs into the interval. Using heatmap-type plots for comparing confidence intervals, we show that the coverage-adjusted intervals have satisfying coverage and shorter expected lengths than competing intervals found in the literature.

  • coverage adjusted confidence intervals for a Binomial Proportion
    arXiv: Methodology, 2012
    Co-Authors: Mans Thulin
    Abstract:

    We consider the classic problem of interval estimation of a Proportion $p$ based on Binomial sampling. The "exact" Clopper-Pearson confidence interval for $p$ is known to be unnecessarily conservative. We propose coverage-adjustments of the Clopper-Pearson interval using prior and posterior distributions of $p$. The adjusted intervals have improved coverage and are often shorter than competing intervals found in the literature. Using new heatmap-type plots for comparing confidence intervals, we find that the coverage-adjusted intervals are particularly suitable for $p$ close to 0 or 1.

Lawrence D Brown - One of the best experts on this subject based on the ideXlab platform.

  • confidence intervals for a Binomial Proportion and asymptotic expansions
    Annals of Statistics, 2002
    Co-Authors: Lawrence D Brown, Anirban Dasgupta
    Abstract:

    p ± zα/2n −1/2 ( ˆ p(1 −ˆ p)) 1/2 is currently in near universal use. We first show that the coverage properties of the Wald interval are persistently poor and defy virtually all conventional wisdom. We then proceed to a theoretical comparison of the standard interval and four additional alternative intervals by asymptotic expansions of their coverage probabilities and expected lengths. The four additional interval methods we study in detail are the score-test interval (Wilson), the likelihood-ratio-test interval, a Jeffreys prior Bayesian interval and an interval suggested by Agresti and Coull. The asymptotic expansions for coverage show that the first three of these alternative methods have coverages that fluctuate about the nominal value, while the Agresti– Coull interval has a somewhat larger and more nearly conservative coverage function. For the five interval methods we also investigate asymptotically their average coverage relative to distributions for p supported within (0, 1). In terms of expected length, asymptotic expansions show that the Agresti– Coull interval is always the longest of these. The remaining three are rather comparable and are shorter than the Wald interval except for p near 0 or 1. These analytical calculations support and complement the findings and the recommendations in Brown, Cai and DasGupta (Statist. Sci. (2001) 16 101–133).

  • interval estimation for a Binomial Proportion
    Statistical Science, 2001
    Co-Authors: Lawrence D Brown, Anirban Dasgupta
    Abstract:

    We revisit the problem of interval estimation of a Binomial Proportion. The erratic behavior of the coverage probability of the stan- d ardWaldconfid ence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that the chaotic coverage properties of the Waldinter- val are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects andcannot be trusted . This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and con- text. Each interval is examinedfor its coverage probability andits length. Basedon this analysis, we recommendthe Wilson interval or the equal- tailedJeffreys prior interval for small n andthe interval suggestedin Agresti andCoull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.