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UNIFORM CONVERGENCE RATES FOR NONPARAMETRIC ESTIMATORS OF A DENSITY FUNCTION AND ITS DERIVATIVES WHEN THE DENSITY HAS A KNOWN POLE.

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Τίτλος: UNIFORM CONVERGENCE RATES FOR NONPARAMETRIC ESTIMATORS OF A DENSITY FUNCTION AND ITS DERIVATIVES WHEN THE DENSITY HAS A KNOWN POLE.
Συγγραφείς: Srisuma, Sorawoot1 (AUTHOR) s.srisuma@nus.edu.sg
Πηγή: Econometric Theory. Jun2026, Vol. 42 Issue 3, p631-657. 27p.
Θεματικοί όροι: *Econometrics, *Economic models, Nonparametric estimation, Probability density function, Derivatives (Mathematics)
Περίληψη: We study the uniform convergence rates of nonparametric estimators for a probability density function and its derivatives when the density has a known pole. Such situations arise in some structural microeconometric models, for example, in auction, labor, and consumer search, where uniform convergence rates of density functions are important for nonparametric and semiparametric estimation. Existing uniform convergence rates based on Rosenblatt's kernel estimator are derived under the assumption that the density is bounded. They are not applicable when there is a pole in the density. We treat the pole nonparametrically and show various kernel-based estimators can attain any convergence rate that is slower than the optimal rate when the density is bounded uniformly over an appropriately expanding support under mild conditions. [ABSTRACT FROM AUTHOR]
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  Data: UNIFORM CONVERGENCE RATES FOR NONPARAMETRIC ESTIMATORS OF A DENSITY FUNCTION AND ITS DERIVATIVES WHEN THE DENSITY HAS A KNOWN POLE.
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  Data: We study the uniform convergence rates of nonparametric estimators for a probability density function and its derivatives when the density has a known pole. Such situations arise in some structural microeconometric models, for example, in auction, labor, and consumer search, where uniform convergence rates of density functions are important for nonparametric and semiparametric estimation. Existing uniform convergence rates based on Rosenblatt's kernel estimator are derived under the assumption that the density is bounded. They are not applicable when there is a pole in the density. We treat the pole nonparametrically and show various kernel-based estimators can attain any convergence rate that is slower than the optimal rate when the density is bounded uniformly over an appropriately expanding support under mild conditions. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Econometric Theory is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1017/S0266466625100030
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      – Code: eng
        Text: English
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      – SubjectFull: Econometrics
        Type: general
      – SubjectFull: Economic models
        Type: general
      – SubjectFull: Nonparametric estimation
        Type: general
      – SubjectFull: Probability density function
        Type: general
      – SubjectFull: Derivatives (Mathematics)
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      – TitleFull: UNIFORM CONVERGENCE RATES FOR NONPARAMETRIC ESTIMATORS OF A DENSITY FUNCTION AND ITS DERIVATIVES WHEN THE DENSITY HAS A KNOWN POLE.
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              M: 06
              Text: Jun2026
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              Y: 2026
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