Abstract
Kernel-type nonparametric estimates of Poisson regression function are considered. We establish the conditions of uniform consistency and the limit theorems for continuous functionals connected with this function on \(C[a,1-a]\), \(0<a<\frac{1}{2}\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
References
S. Efromovich, Nonparametric curve estimation. Methods, theory, and applications. Springer Series in Statistics. Springer-Verlag, New York, 1999.
M. Kohler and A. Krzyżak, Asymptotic confidence intervals for Poisson regression. J. Multivariate Anal. 98 (2007), no. 5, 1072–1094.
C.-H. Hwang and J.-Y. Shim, Semiparametric kernel Poisson regression for longitudinal count data. Commun. Stat. Appl. Methods 15 (2008), no. 1003–1011.
Y. Pawitan and F. O’Sullivan, Data-dependent bandwidth selection for emission computed tomography reconstruction. IEEE Transactions on Medical Imaging 12 (1993), no. 2, 167–172.
E. D. Kolaczyk, Nonparametric Estimation of Gamma-Ray Burst intensities using Haar wavelets. The Astrophysical Journal 483 (1997), no. 1, 340–349.
E. A. Nadaraja, On a regression estimate. (Russian) Teor. Verojatnost. i Primenen. 9 (1964), 157–159.
G. S. Watson, Smooth regression analysis. Sankhya Ser. A 26 (1964), 359–372.
P. K. Babilua, E. A. Nadaraya and G. A. Sokhadze, On the square-integrable measure of the divergence of two nuclear estimations of the Bernoulli regression functions. Translation of Ukraïn. Mat. Zh. 67 (2015), no. 1, 3–18; Ukrainian Math. J. 67 (2015), no. 1, 1–18.
P. Whittle, Bounds for the moments of linear and quadratic forms in independent variables. Teor. Verojatnost. i Primenen. 5 (1960), 331–335.
A. N. Shiryaev, Problems of Probability. Izd. MTSNMO, 2014.
E. A. Nadaraya and R. M. Absava, Some Problems of the Theory of Nonparametric Estimation of Functional Characteristics of the Observations Distribution Law. (Russian) Tbilisi University Press, Tbilisi, 2008.
J. D. Hart and T. E. Wehrly, Kernel regression when the boundary region is large, with an application to testing the adequacy of polynomial models. J. Amer. Statist. Assoc. 87 (1992), no. 420, 1018–1024.
I. I. Gikhman and A. V. Skorohod, Introduction to the Theory of Random Processes. (Russian) Izdat. “Nauka”, Moscow 1965.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Babilua, P., Nadaraya, E. UNIFORM CONVERGENCE OF A NONPARAMETRIC ESTIMATE OF POISSON REGRESSION WITH AN APPLICATION TO GOODNESS-OF-FIT. J Math Sci (2024). https://doi.org/10.1007/s10958-024-07035-x
Accepted:
Published:
DOI: https://doi.org/10.1007/s10958-024-07035-x