Outlier detection under a covariate-adjusted exponential regression model with censored data

• Published in: Computational statistics Vol. 36; no. 2; pp. 961 - 976
• Main Authors: Pan, Yingli, Liu, Zhan, Song, Guangyu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021; Springer Nature B.V
• Subjects: Algorithms; Applied statistics; Breast cancer; Data analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematics and Statistics; Original Paper; Outliers (statistics); Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Regression coefficients; Regression models; Regularization; Statistics; Outlier diagnosis; SCAD; Coordinate descent algorithm; Contaminated covariate
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-020-01052-5

Exponential regression models with censored data are most widely used in practice. In the modeling process, there exist situations where the covariates are not directly observed but are observed after being contaminated by unknown functions of an observable confounder in a multiplicative manner. The problem of outlier detection is a fundamental and important problem in applied statistics. In this paper, we use a nonparametric regression method to adjust the covariates and recast the outlier detection issue into a high-dimensional regularization regression issue in the covariate-adjusted exponential regression model with censored data. We propose a smoothly clipped absolute deviation (SCAD) penalized likelihood method to detect the possible outliers, which features that the proposed method can simultaneously deal with outlier detection and estimations for the regression coefficients. The coordinate descent algorithm is employed to facilitate computation. Simulation studies are conducted to evaluate the finite-sample performance of our proposed method. An application to a German breast cancer study demonstrates the utility of the proposed method in practice.