Cook’s Distance Measures for Varying Coefficient Models With Functional Responses

The aim of this article is to develop Cook’s distance measures for assessing the influence of both atypical curves and observations under varying coefficient model with functional responses. Our Cook’s distance measures include Cook’s distances for deleting multiple curves and for deleting multiple grid points, and their scaled Cook’s distances. We systematically investigate some theoretical properties of these diagnostic measures. Simulation studies are conducted to evaluate the finite sample properties of these Cook’s distances under different scenarios. A real diffusion tensor tract dataset is analyzed to illustrate the use of our diagnostic measures.

[1]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[2]  Anthony C. Davison,et al.  Regression model diagnostics , 1992 .

[3]  Stanley R. Johnson,et al.  Varying Coefficient Models , 1984 .

[4]  Bo-Cheng Wei,et al.  Case-deletion measures for models with incomplete data , 2001 .

[5]  Jeng-Min Chiou,et al.  Diagnostics for functional regression via residual processes , 2007, Comput. Stat. Data Anal..

[6]  Qing Shen,et al.  Diagnostics for Linear Models With Functional Responses , 2007, Technometrics.

[7]  Jin-Ting Zhang,et al.  Statistical inferences for functional data , 2007, 0708.2207.

[8]  R. Dennis Cook,et al.  Detection of Influential Observation in Linear Regression , 2000, Technometrics.

[9]  Choongrak Kim,et al.  Cook's distance in local polynomial regression , 2001 .

[10]  Hongtu Zhu,et al.  PERTURBATION AND SCALED COOK'S DISTANCE. , 2012, Annals of statistics.

[11]  J. Faraway.  Regression analysis for a functional response , 1997 .

[12]  Bo-Cheng Wei,et al.  Exponential Family Nonlinear Models , 1998 .

[13]  Martin Styner,et al.  FADTTS: Functional analysis of diffusion tensor tract statistics , 2011, NeuroImage.

[14]  Julian J. Faraway,et al.  An F test for linear models with functional responses , 2004 .

[15]  Jianqing Fan,et al.  Statistical Methods with Varying Coefficient Models. , 2008, Statistics and its interface.

[16]  Runze Li,et al.  MULTIVARIATE VARYING COEFFICIENT MODEL FOR FUNCTIONAL RESPONSES. , 2012, Annals of statistics.

[17]  Sheng-Tsaing Tseng,et al.  Outlier detection in general profiles using penalized regression method , 2014 .

[18]  Martin Styner,et al.  FRATS: Functional Regression Analysis of DTI Tract Statistics , 2010, IEEE Transactions on Medical Imaging.

[19]  H. Müller,et al.  Functional Data Analysis for Sparse Longitudinal Data , 2005 .