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Nonparametric estimation of the shape functions and related asymptotic results

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  • M. D. Jiménez-Gamero

    (Universidad de Sevilla)

  • J. C. Pardo-Fernández

    (Universidade de Vigo)

Abstract

Arriaza et al (Metrika 82:99–124, 2019) introduced the right and left shape functions, which enjoy interesting properties in terms of describing the global form of a distribution. This paper proposes and studies nonparametric estimators of those functions. The estimators involve nonparametric estimation of the quantile and density functions. Pointwise and uniform consistency are proved under general regularity assumptions, as well as the limit in law. Simulations are included to study the practical performance of the proposed estimators. The analysis of a real data set illustrates the methodology.

Suggested Citation

  • M. D. Jiménez-Gamero & J. C. Pardo-Fernández, 2024. "Nonparametric estimation of the shape functions and related asymptotic results," Statistical Papers, Springer, vol. 65(3), pages 1575-1611, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01456-7
    DOI: 10.1007/s00362-023-01456-7
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    1. Eustasio Barrio & Juan Cuesta-Albertos & Carlos Matrán & Sándor Csörgö & Carles Cuadras & Tertius Wet & Evarist Giné & Richard Lockhart & Axel Munk & Winfried Stute, 2000. "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 1-96, June.
    2. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    3. Gómez-Déniz, Emilio & Sordo, Miguel A. & Calderín-Ojeda, Enrique, 2014. "The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 49-57.
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