Data-driven local bandwidth selection for additive models with missing data

This paper deals in the nonparametric estimation of additive models in the presence of missing data in the response variable. Specifically in the case of additive models estimated by the Backfitting algorithm with local polynomial smoothers [1]. Three estimators are presented, one based on the available data and two based on a complete sample from imputation techniques. We also develop a data-driven local bandwidth selector based on a Wild Bootstrap approximation of the mean squared error of the estimators. The performance of the estimators and the local bootstrap bandwidth selection method are explored through simulation experiments.

[1]  J. Ibrahim,et al.  Model Selection Criteria for Missing-Data Problems Using the EM Algorithm , 2008, Journal of the American Statistical Association.

[2]  Jean D. Opsomer,et al.  Asymptotic Properties of Backfitting Estimators , 2000 .

[3]  Oliver Linton,et al.  Integration and backfitting methods in additive models-finite sample properties and comparison , 1999 .

[4]  R. Tibshirani,et al.  Linear Smoothers and Additive Models , 1989 .

[5]  J. Ibrahim.  Incomplete Data in Generalized Linear Models , 1990 .

[6]  Graciela Boente,et al.  Robust nonparametric estimation with missing data , 2009 .

[7]  Joseph G. Ibrahim,et al.  Missing data methods in longitudinal studies: a review , 2009 .

[8]  Thomas Nittner,et al.  The additive model affected by missing completely at random in the covariate , 2004, Comput. Stat..

[9]  Roderick J. A. Little.  Regression with Missing X's: A Review , 1992 .

[10]  J. P. Albaladejo,et al.  Métodos de inferencia estadística con datos faltantes: estudio de simulación sobre los efectos en las estimaciones. , 2006 .

[11]  Philip E. Cheng,et al.  Applications of kernel regression estimation:survey , 1990 .

[12]  Philip E. Cheng,et al.  Nonparametric regression estimation with missing data , 1995 .

[13]  E. Nadaraya.  On Estimating Regression , 1964 .

[14]  Roger A. Sugden,et al.  Multiple Imputation for Nonresponse in Surveys , 1988 .

[15]  C. Fuchs.  Maximum Likelihood Estimation and Model Selection in Contingency Tables with Missing Data , 1982 .

[16]  M. D. Martínez-Miranda,et al.  A Bootstrap Local Bandwidth Selector for Additive Models , 2008 .

[17]  Enno Mammen,et al.  The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions , 1999 .

[18]  Joel L. Horowitz,et al.  Optimal estimation in additive regression models , 2006 .

[19]  S. Lipsitz,et al.  Missing responses in generalised linear mixed models when the missing data mechanism is nonignorable , 2001 .

[20]  Søren Feodor Nielsen,et al.  Nonparametric conditional mean imputation , 2001 .

[21]  Enno Mammen,et al.  Bandwidth selection for smooth backfitting in additive models , 2005, math/0507425.

[22]  Wenceslao González-Manteiga,et al.  Nonparametric Mean Estimation with Missing Data , 2004 .

[23]  D. M. Titterington,et al.  Imputation of missing values using density estimation , 1989 .

[24]  Joseph G. Ibrahim,et al.  Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable , 1999 .

[25]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[26]  O. Linton,et al.  A kernel method of estimating structured nonparametric regression based on marginal integration , 1995 .

[27]  G Molenberghs,et al.  Model selection for incomplete and design‐based samples , 2006, Statistics in medicine.

[28]  María Dolores Martínez Miranda,et al.  The choice of smoothing parameter in nonparametric regression through Wild Bootstrap , 2004, Comput. Stat. Data Anal..

[29]  Geert Molenberghs,et al.  Local multiple imputation , 2002 .

[30]  Dag Tjøstheim,et al.  Nonparametric Identification of Nonlinear Time Series: Projections , 1994 .

[31]  Jens Perch Nielsen,et al.  Smooth backfitting in practice , 2005 .

[32]  Philip E. Cheng,et al.  Nonparametric Estimation of Mean Functionals with Data Missing at Random , 1994 .

[33]  Raymond J. Carroll,et al.  Local Linear Regression for Generalized Linear Models with Missing Data , 1998 .

[34]  J. Ibrahim,et al.  Semiparametric Models for Missing Covariate and Response Data in Regression Models , 2006, Biometrics.

[35]  D. M. Titterington,et al.  Kernel‐Based Density Estimates from Incomplete Data , 1983 .

[36]  Werner Vach,et al.  Logistic Regression with Missing Values in the Covariates , 1994 .

[37]  J. Neyman.  Contribution to the Theory of Sampling Human Populations , 1938 .

[39]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[40]  L. Zhao,et al.  Weighted Semiparametric Estimation in Regression Analysis with Missing Covariate Data , 1997 .

[41]  David Ruppert,et al.  Fitting a Bivariate Additive Model by Local Polynomial Regression , 1997 .