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Simulation-Based Confidence Intervals for Functions With Complicated Derivatives

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  • Micha Mandel

Abstract

In many scientific problems, the quantity of interest is a function of parameters that index the model, and confidence intervals are constructed by applying the delta method. However, when the function of interest has complicated derivatives, this standard approach is unattractive and alternative algorithms are required. This article discusses a simple simulation-based algorithm for estimating the variance of a transformation, and demonstrates its simplicity and accuracy by applying it to several statistical problems.

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  • Micha Mandel, 2013. "Simulation-Based Confidence Intervals for Functions With Complicated Derivatives," The American Statistician, Taylor & Francis Journals, vol. 67(2), pages 76-81, May.
    • Handle: RePEc:taf:amstat:v:67:y:2013:i:2:p:76-81
    DOI: 10.1080/00031305.2013.783880
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    Cited by:

    1. Jackson, Christopher, 2016. "flexsurv: A Platform for Parametric Survival Modeling in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i08).
    2. José H. Dias Gonçalves & João J. Ferreira Gomes & Lihki Rubio & Filipe R. Ramos, 2023. "A Generalized Log Gamma Approach: Theoretical Contributions and an Application to Companies’ Life Expectancy," Mathematics, MDPI, vol. 11(23), pages 1-23, November.
    3. Ardo Hout & Graciela Muniz-Terrera, 2019. "Hidden three-state survival model for bivariate longitudinal count data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 529-545, July.
    4. Rincon, Diego F. & Esch, Evan D. & Gutierrez-Illan, Javier & Tesche, Melissa & Crowder, David W., 2024. "Predicting insect population dynamics by linking phenology models and monitoring data," Ecological Modelling, Elsevier, vol. 493(C).
    5. Signe M Jensen & Hanne Hauger & Christian Ritz, 2018. "Mediation analysis for logistic regression with interactions: Application of a surrogate marker in ophthalmology," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-7, February.
    6. Touraine, Célia & Gerds, Thomas A. & Joly, Pierre, 2017. "SmoothHazard: An R Package for Fitting Regression Models to Interval-Censored Observations of Illness-Death Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i07).
    7. Kahle, David J. & Young, Phil D. & Greer, Brandi A. & Young, Dean M., 2016. "Confidence intervals for the ratio of two Poisson rates under one-way differential misclassification using double sampling," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 122-132.

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