Sensitivity analysis of partially linear models with response missing at random

ABSTRACT This article investigates case-deletion influence analysis via Cook’s distance and local influence analysis via conformal normal curvature for partially linear models with response missing at random. Local influence approach is developed to assess the sensitivity of parameter and nonparametric estimators to various perturbations such as case-weight, response variable, explanatory variable, and parameter perturbations on the basis of semiparametric estimating equations, which are constructed using the inverse probability weighted approach, rather than likelihood function. Residual and generalized leverage are also defined. Simulation studies and a dataset taken from the AIDS Clinical Trials are used to illustrate the proposed methods.

[1]  Jack Cuzick,et al.  Efficient Estimates in Semiparametric Additive Regression Models with Unknown Error Distribution , 1992 .

[2]  Zhihua Sun,et al.  Estimation in partially linear models with missing responses at random , 2007 .

[3]  Xuming He,et al.  Local Influence Analysis for Penalized Gaussian Likelihood Estimators in Partially Linear Models , 2003 .

[4]  Hongtu Zhu,et al.  Bayesian Sensitivity Analysis of Statistical Models with Missing Data. , 2014, Statistica Sinica.

[5]  P. Speckman.  Kernel smoothing in partial linear models , 1988 .

[6]  W. Fung,et al.  Generalized Leverage and its Applications , 1998 .

[7]  Yanyuan Ma,et al.  Efficient semiparametric estimator for heteroscedastic partially linear models , 2006 .

[8]  Xing Chen,et al.  Local influence analysis of nonlinear structural equation models with nonignorable missing outcomes from reproductive dispersion models , 2009, Comput. Stat. Data Anal..

[9]  Qi Li,et al.  Efficient estimation of a semiparametric partially linear varying coefficient model , 2005, math/0504510.

[10]  Hung Chen,et al.  A two-stage spline smoothing method for partially linear models , 1991 .

[11]  Clive W. J. Granger,et al.  Semiparametric estimates of the relation between weather and electricity sales , 1986 .

[12]  M. Davidian,et al.  Covariate adjustment for two‐sample treatment comparisons in randomized clinical trials: A principled yet flexible approach , 2008, Statistics in medicine.

[13]  A. Troxel,et al.  Statistical analysis of quality of life with missing data in cancer clinical trials. , 1998, Statistics in medicine.

[14]  Joseph G Ibrahim,et al.  Local Influence for Generalized Linear Models with Missing Covariates , 2009, Biometrics.

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

[16]  J. Ibrahim,et al.  Bayesian local influence for survival models , 2011, Lifetime data analysis.

[17]  A. Troxel,et al.  AN INDEX OF LOCAL SENSITIVITY TO NONIGNORABILITY , 2004 .

[18]  Yat Sun Poon,et al.  Conformal normal curvature and assessment of local influence , 1999 .

[19]  Nancy E. Heckman,et al.  Spline Smoothing in a Partly Linear Model , 1986 .

[20]  Nicole A. Lazar,et al.  Statistical Analysis With Missing Data , 2003, Technometrics.

[21]  G. Boente,et al.  Robust estimates in generalized partially linear models , 2006, 0708.0165.

[22]  Sik-Yum Lee,et al.  Local influence for incomplete data models , 2001 .

[23]  R. Cook.  Assessment of Local Influence , 1986 .

[24]  J. Ibrahim,et al.  Bayesian influence analysis: a geometric approach. , 2011, Biometrika.

[25]  Sik-Yum Lee,et al.  Local influence analysis of nonlinear structural equation models , 2004 .