Rapid penalized likelihood-based outlier detection via heteroskedasticity test

ABSTRACT

Outlier detection is fundamental to statistical modelling. When there are multiple outliers, many traditional approaches in use are stepwise detection procedures, which can be computationally expensive and ignore stochastic error in the outlier detection process. Outlier detection can be performed by a heteroskedasticity test. In this article, a rapid outlier detection method via multiple heteroskedasticity test based on penalized likelihood approaches is proposed to handle these kinds of problems. The proposed method detects the heteroskedasticity of all data only by one step and estimate coefficients simultaneously. The proposed approach is distinguished from others in that a rapid modelling approach uses a weighted least squares formulation coupled with nonconvex sparsity-including penalization. Furthermore, the proposed approach does not need to construct test statistics and calculate their distributions. A new algorithm is proposed for optimizing penalized likelihood functions. Favourable theoretical properties of the proposed approach are obtained. Our simulation studies and real data analysis show that the newly proposed methods compare favourably with other traditional outlier detection techniques.

KEYWORDS:

• Difference convex algorithm
• heteroskedasticity test
• linear model
• nonconvex penalized regression
• outlier detection

AMS 2000 SUBJECT CLASSIFICATION:

• 62G08
• 62H99

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by NNSF project (11171188, 11571204, 11231005, 61403419, 11301309, 61403419) of China, NSF project (ZR2014AQ017) of Shandong Province of China, the Fundamental Research Funds for the Central Universities (15CX02083A, 16CX02048A).