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Strict monotonicity of stochastic process extreme distributions

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  • Yang, Lijian

Abstract

Strict monotonicity is proved for the distributions of extremes of processes consisting of series of bounded function with independent random coefficients, in particular for zero mean continuous Gaussian processes over compact metric space. These results have wide applications to global inference problems on unknown functions.

Suggested Citation

  • Yang, Lijian, 2025. "Strict monotonicity of stochastic process extreme distributions," Statistics & Probability Letters, Elsevier, vol. 217(C).
    • Handle: RePEc:eee:stapro:v:217:y:2025:i:c:s016771522400261x
    DOI: 10.1016/j.spl.2024.110292
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    References listed on IDEAS

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    1. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
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    5. Yang, Lijian, 2025. "Continuity of Gaussian extreme distributions," Statistics & Probability Letters, Elsevier, vol. 216(C).
    6. Wang, Jiangyan & Cao, Guanqun & Wang, Li & Yang, Lijian, 2020. "Simultaneous confidence band for stationary covariance function of dense functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    7. Yang, Lijian, 2024. "Exact quantiles of Gaussian process extremes," Statistics & Probability Letters, Elsevier, vol. 213(C).
    8. Kun Huang & Sijie Zheng & Lijian Yang, 2022. "Inference for dependent error functional data with application to event-related potentials," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1100-1120, December.
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