Examination of Influential Observations in Penalized Spline Regression

Turkan S.

11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Greece, 21 - 27 September 2013, vol.1558, pp.1454-1457 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1558
  • Doi Number: 10.1063/1.4825792
  • Country: Greece
  • Page Numbers: pp.1454-1457
  • Hacettepe University Affiliated: Yes


In parametric or nonparametric regression models, the results of regression analysis are affected by some anomalous observations in the data set. Thus, detection of these observations is one of the major steps in regression analysis. These observations are precisely detected by well-known influence measures. Pena's statistic is one of them. In this study, Pena's approach is formulated for penalized spline regression in terms of ordinary residuals and leverages. The real data and artificial data are used to see illustrate the effectiveness of Pena's statistic as to Cook's distance on detecting influential observations. The results of the study clearly reveal that the proposed measure is superior to Cook's Distance to detect these observations in large data set.