Error variance is a measure of the goodness of fit for a regression model. Ahoutou et al. [1] proposed estimators of the error variance under the assumption that the dimension of the nonlinear covariate is one. In this paper, assuming that the dimension of the nonlinear covariate is greater than or equal to 2, we propose estimators of error variance in homogeneous and heterogeneous cases. We propose estimators of the error variance that are constructed without taking atypical values into account and others that are constructed by taking all the data into account. Using simulations, we compare the performance of estimators designed without taking into account atypical values with estimators designed taking into account all the data.

partially linear regression model, atypical values, MSE estimator, U‑statistic, asymptotic normality.

Received: August 2, 2024; Revised: September 4, 2024; Accepted: September 13, 2024

How to cite this article: Belly N. M. AHOUTOU, Armel F. E. YODE and Kouamé F. KOUAKOU, Comparative study of residual variance estimators constructed without or with the presence of atypical values: Case of the partially linear model, Far East Journal of Theoretical Statistics 68(3) (2024), 335-372. https://doi.org/10.17654/0972086324019

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

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