Outlier Detection Using the Outlier Probability for Robust Linear Regression

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	Outlier Detection Using the Outlier Probability for Robust Linear Regression
	Yuen, K. V.; Mu, H.Q.
	2013-12-01
Source Publication	Proceedings of 59th World Statistics Congress
Abstract	Outlier detection is an important problem in statistics. In this paper, we introduce a novel concept of outlier probability for outlier detection and robust linear regression. First, the Mahalanobis distance is utilized to identify the leverage points. By excluding the leverage points, the maximum trimmed likelihood estimation will be used to obtain an initial set of regular data points while the remaining and the leverage points are included in the initial suspicious data set. Then, each suspicious data point and the combinations are evaluated by a novel outlier probability that depends not only on the residuals but also the size of the data set. Incorporating the data size is important as it controls the probability of the existence of a data point (or a batch or data points) exceeding a given value of the normalized residual. This outlier probability is robust because it incorporates also the posterior uncertainty quantified using the Bayesian approach. Then, the data points with outlier probability below 0.5 will be transferred to the set of regular data points. Iteration is continued until all suspicious data points are associated with outlier probability over 0.5. Finally, robust regression can be conducted by considering only the set of regular points. Therefore, it is expected that the parametric identification results are robust to outliers. In contrast to other existing outlier detection criteria that require some subjective threshold (e.g., normalized residual larger than 2.5), the outlier probability criterion of 0.5 is objective. Finally, a challenging application will be presented and comparison to other well-known methods will be given.
Keyword	Bayesian inference leverage inverse problem outlier robust analysis system identification
Language	英語English
The Source to Article	PB_Publication
PUB ID	33813
Document Type	Conference paper
Collection	GRADUATE SCHOOL
Corresponding Author	Yuen, K. V.
Recommended Citation GB/T 7714	Yuen, K. V.,Mu, H.Q.. Outlier Detection Using the Outlier Probability for Robust Linear Regression[C], 2013.
APA	Yuen, K. V.., & Mu, H.Q. (2013). Outlier Detection Using the Outlier Probability for Robust Linear Regression. Proceedings of 59th World Statistics Congress.

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