- 期刊
- OpenAccess
A Heteroscedastic Method for Comparing Regression Lines at Specified Design Points When Using a Robust Regression Estimator
並列摘要
It is well known that the ordinary least squares (OLS) regression estimator is not robust. Many robust regression estimators have been proposed and inferential methods based on these estimators have been derived. However, for two independent groups, let θj(X) be some conditional measure of location for the jth group, given X, based on some robust regression estimator. An issue that has not been addressed is computing a 1-α confidence interval for θ1(X)-θ2(X) in a manner that allows both within group and between group hetereoscedasticity. The paper reports the finite sample properties of a simple method for accomplishing this goal. Simulations indicate that, in terms of controlling the probability of a Type I error, the method performs very well for a wide range of situations, even with a relatively small sample size. In principle, any robust regression estimator can be used. The simulations are focused primarily on the Theil-Sen estimator, but some results using Yohai's MM-estimator, as well as the Koenker and Bassett quantile regression estimator, are noted. Data from the Well Elderly II study, dealing with measures of meaningful activity using the cortisol awakening response as a covariate, are used to illustrate that the choice between an extant method based on a nonparametric regression estimator, and the method suggested here, can make a practical difference.
被引用紀錄
延伸閱讀
- 薛惠娟（2010）。Power comparison about repeated measures, hierarchical linear model and regression model in analyzing longitudinal data with missing values〔碩士論文，國立臺北大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0023-2007201018421600
- Yang, Y. H. (2020). Coefficient Estimation for Regression Models with Time Series and Heteroscedastic Errors and Its Application to High-Dimensional Model Selection [master's thesis, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-2502202114232019
- Tu, Y. K., & Chan, C. P. (2002). Mathematical Coupling of Data in Periodontal Research : Illustrations of Misleading Results in Correlation/Regression Analysis. 中華民國牙周病醫學會雜誌, 7(1), 23-36. https://www.airitilibrary.com/Article/Detail?DocID=10279962-200203-7-1-23-36-a
- Polat, E., & Gunay, S. (2015). The Comparison of Partial Least Squares Regression, Principal Component Regression and Ridge Regression with Multiple Linear Regression for Predicting PM10 Concentration Level based on Meteorological Parameters. Journal of Data Science, 13(4), 663-692. https://doi.org/10.6339/JDS.201510_13(4).0003
- Yang, S. P. (2014). A class of generalized ridge estimator for high-dimensional linear regression [master's thesis, National Central University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0031-0412201512000945