EXACT DISTRIBUTION OF HAT VALUES AND IDENTIFICATION OF LEVERAGE POINTS

  • G.S. David Sam Jayakumar Jamal Institute of Management, Tiruchirappalli – 620 020, India
  • A. Sulthan Jamal Institute of Management, Tiruchirappalli – 620 020, India
Keywords: Centered Hat Values, Hat Matrix, Beta-Distribution, Moments, Leverage Points, Outliers, X-Space

Abstract

This paper proposed the exact distribution of centered hat values of the hat matrix of predictors in multiple linear regression analysis. The authors adopted the relationship proposed by Belsey et al. (1980) between the centered hat values and the F-ratio and we showed that the derived density function of the centered hat values followed Beta distribution (p1,np) and it lies between1/ 1 ii nh  . Moreover, the first two moments of the distribution are derived and we established the upper and lower limits of the centered hat values. Moreover, the shape of the density function of hat values is also visualized and the authors computed the percentage points of centered hat values at 5% and 1% significance level for different sample sizes and predictors. Finally, the authors proposed two approaches. The first approach helps to identify the leverage points in multiple linear regression analysis in the X-space based on the test of significance and the second approach scrutinized the leverage points as well as the outliers. The proposed approaches were numerically illustrated and the results were compared the traditional approach.

 

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Published
2014-06-16
Section
Articles