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Far East Journal of Theoretical Statistics

Far East Journal of Theoretical Statistics
Volume 69, Issue 2 , Pages 189 - 203 (August 2025)
http://dx.doi.org/10.17654/0972086325009

CLASSES OF ADAPTIVE ESTIMATORS TO NONPARAMETRIC REGRESSION

Sharada V. Bhat and Shrinath M. Bijjargi

Abstract:

Classes of adaptive kernel regression estimators are developed under nonparametric regression. These estimators are based on varying bandwidths which are dependent on pilot densities and functions of order statistic. The distributional properties of these estimators are derived. The performance is evaluated through simulation studies. Also, we obtain confidence bands for the proposed estimators and illustrate their application with an example.

Keywords and phrases:

adaptive estimator, nonparametric regression, quasi-range, varying bandwidth, pilot density, confidence bands

Received: March 4, 2025; Accepted: May 12, 2025; Published: June 25, 2025

How to cite this article: Sharada V. Bhat and Shrinath M. Bijjargi, Classes of adaptive estimators to nonparametric regression, Far East Journal of Theoretical Statistics 69(2) (2025), 189‑203. https://doi.org/10.17654/0972086325009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1]I. S. Abramson, On bandwidth variation in kernel estimates-a square root law, Ann. Statist. 10(4) (1982), 1217-1223.

[2]T. H. Ali, Modification of the adaptive Nadaraya-Watson kernel method for nonparametric regression (simulation study), Comm. Statist. Simulation Comput. 51(2) (2022), 391-403.

[3]K. H. Aljuhani and Turk Al, Modification of the adaptive Nadaraya-Watson kernel regression estimator, Scientific Research and Essays 9(22) (2014), 966-971.

[4]S. V. Bhat and B. Deshpande, A generalized class of varying kernel regression estimators, International Journal of Computational and Theoretical Statistics 6(2) (2019), 155-163.

[5]S. Demir and O. Toktamiş, On the adaptive Nadaraya-Watson kernel regression estimators, Hacet. J. Math. Stat. 39(3) (2010), 429-437.

[6]B. Deshpande, Some contributions to nonparametric regression, Ph.D. Thesis, Karnatak University, Dharwad, India, 2019.

[7]B. Deshpande and S. V. Bhat, Random design kernel regression estimator, International Journal of Agricultural and Statistical Sciences 15(1) (2019), 11-17.

[8]V. B. Joshi and B. Deshpande, A new modification to the adaptive Nadaraya-Watson kernel regression estimator, Adv. Appl. Stat. 49(4) (2016), 245-256.

[9]D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis, John Wiley & Sons, 2003.

[10]E. A. Nadaraya, On estimating regression, Theory Probab. Appl. 9(1) (1964), 141-142.

[11]D. W. Scott and G. R. Terrell, Biased and unbiased cross-validation in density estimation, J. Amer. Statist. Assoc. 82(400) (1987), 1131-1146.

[12]B. W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall/CRC Press, 1986.

[13]G. S. Watson, Smooth regression analysis, Sankhyā Ser. A 26(4) (1964), 359-372.

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