Pena's statistic for the Liu regression

ABSTRACT

In fitting regression model, one or more observations may have substantial effects on estimators. These unusual observations are precisely detected by a new diagnostic measure, Pena's statistic. In this article, we introduce a type of Pena's statistic for each point in Liu regression. Using the forecast change property, we simplify the Pena's statistic in a numerical sense. It is found that the simplified Pena's statistic behaves quite well as far as detection of influential observations is concerned. We express Pena's statistic in terms of the Liu leverages and residuals. The normality of this statistic is also discussed and it is demonstrated that it can identify a subset of high Liu leverage outliers. For numerical evaluation, simulated studies are given and a real data set has been analysed for illustration.

KEYWORDS:

• Case deletion
• Cook’s distance
• influential observation
• Liu estimator
• Pena’s statistic

AMS CLASSIFICATIONS:

• 62J20
• 62J12

Disclosure statement

No potential conflict of interest was reported by the authors.