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Inference for Monotone Functions Under Short- and Long-Range Dependence: Confidence Intervals and New Universal Limits

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  • Pramita Bagchi
  • Moulinath Banerjee
  • Stilian A. Stoev

Abstract

We introduce new point-wise confidence interval estimates for monotone functions observed with additive, dependent noise. Our methodology applies to both short- and long-range dependence regimes for the errors. The interval estimates are obtained via the method of inversion of certain discrepancy statistics. This approach avoids the estimation of nuisance parameters such as the derivative of the unknown function, which previous methods are forced to deal with. The resulting estimates are therefore more accurate, stable, and widely applicable in practice under minimal assumptions on the trend and error structure. The dependence of the errors especially long-range dependence leads to new phenomena, where new universal limits based on convex minorant functionals of drifted fractional Brownian motion emerge. Some extensions to uniform confidence bands are also developed. Supplementary materials for this article are available online.

Suggested Citation

  • Pramita Bagchi & Moulinath Banerjee & Stilian A. Stoev, 2016. "Inference for Monotone Functions Under Short- and Long-Range Dependence: Confidence Intervals and New Universal Limits," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1634-1647, October.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:516:p:1634-1647
    DOI: 10.1080/01621459.2015.1100622
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    Cited by:

    1. Pramita Bagchi & Subhra Sankar Dhar, 2020. "A study on the least squares estimator of multivariate isotonic regression function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1192-1221, December.
    2. Matias D. Cattaneo & Michael Jansson & Kenichi Nagasawa, 2020. "Bootstrap‐Based Inference for Cube Root Asymptotics," Econometrica, Econometric Society, vol. 88(5), pages 2203-2219, September.

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