Better confidence intervals for the slope parameters of the quadratic regression model when the error term is not normally distributed
Апстракт
When the error term is not normally distributed, the confidence intervals for the slope parameters of the quadratic regression model, based on the ordinary t-statistic, are not appropriate. In this paper, we consider the interval based on the ordinary t-statistic and the intervals based on the resampling methods. Further, we derive the Edgeworth expansion of the distribution of the t-statistic. Based on that expansion we propose a new transformation of the t-statistic which is used for the construction of the bootstrap-t confidence interval for the slope parameter beta(2). The obtained results for the Gamma, Weibull, and Exponential distributions and for the real data set show that the intervals based on the resampling methods and the interval based on the new transformation of the t-statistic provide better coverage accuracy than the interval based on the ordinary t-statistic.
Кључне речи:
t-statistic / Resampling methods / Quadratic regression model / Edgeworth expansion of the distribution of the t-statistic / Coverage accuracy / Confidence intervals for the slope parametersИзвор:
Communications in Statistics-Simulation and Computation, 2022Издавач:
- Taylor & Francis Inc, Philadelphia
DOI: 10.1080/03610918.2022.2120201
ISSN: 0361-0918
WoS: 000851623400001
Scopus: 2-s2.0-85138283641
Институција/група
Fakultet organizacionih naukaTY - JOUR AU - Rajić, Vesna AU - Ivković, Ivana AU - Li, Wei AU - Lazović, Rade PY - 2022 UR - https://rfos.fon.bg.ac.rs/handle/123456789/2351 AB - When the error term is not normally distributed, the confidence intervals for the slope parameters of the quadratic regression model, based on the ordinary t-statistic, are not appropriate. In this paper, we consider the interval based on the ordinary t-statistic and the intervals based on the resampling methods. Further, we derive the Edgeworth expansion of the distribution of the t-statistic. Based on that expansion we propose a new transformation of the t-statistic which is used for the construction of the bootstrap-t confidence interval for the slope parameter beta(2). The obtained results for the Gamma, Weibull, and Exponential distributions and for the real data set show that the intervals based on the resampling methods and the interval based on the new transformation of the t-statistic provide better coverage accuracy than the interval based on the ordinary t-statistic. PB - Taylor & Francis Inc, Philadelphia T2 - Communications in Statistics-Simulation and Computation T1 - Better confidence intervals for the slope parameters of the quadratic regression model when the error term is not normally distributed DO - 10.1080/03610918.2022.2120201 UR - conv_2759 ER -
@article{ author = "Rajić, Vesna and Ivković, Ivana and Li, Wei and Lazović, Rade", year = "2022", abstract = "When the error term is not normally distributed, the confidence intervals for the slope parameters of the quadratic regression model, based on the ordinary t-statistic, are not appropriate. In this paper, we consider the interval based on the ordinary t-statistic and the intervals based on the resampling methods. Further, we derive the Edgeworth expansion of the distribution of the t-statistic. Based on that expansion we propose a new transformation of the t-statistic which is used for the construction of the bootstrap-t confidence interval for the slope parameter beta(2). The obtained results for the Gamma, Weibull, and Exponential distributions and for the real data set show that the intervals based on the resampling methods and the interval based on the new transformation of the t-statistic provide better coverage accuracy than the interval based on the ordinary t-statistic.", publisher = "Taylor & Francis Inc, Philadelphia", journal = "Communications in Statistics-Simulation and Computation", title = "Better confidence intervals for the slope parameters of the quadratic regression model when the error term is not normally distributed", doi = "10.1080/03610918.2022.2120201", url = "conv_2759" }
Rajić, V., Ivković, I., Li, W.,& Lazović, R.. (2022). Better confidence intervals for the slope parameters of the quadratic regression model when the error term is not normally distributed. in Communications in Statistics-Simulation and Computation Taylor & Francis Inc, Philadelphia.. https://doi.org/10.1080/03610918.2022.2120201 conv_2759
Rajić V, Ivković I, Li W, Lazović R. Better confidence intervals for the slope parameters of the quadratic regression model when the error term is not normally distributed. in Communications in Statistics-Simulation and Computation. 2022;. doi:10.1080/03610918.2022.2120201 conv_2759 .
Rajić, Vesna, Ivković, Ivana, Li, Wei, Lazović, Rade, "Better confidence intervals for the slope parameters of the quadratic regression model when the error term is not normally distributed" in Communications in Statistics-Simulation and Computation (2022), https://doi.org/10.1080/03610918.2022.2120201 ., conv_2759 .