Feasible estimation in generalized structured models

This article introduces a feasible estimation method for a large class of semi and nonparametric models. We present the family of generalized structured models which we wish to estimate. After highlighting the main idea of the theoretical smooth backfitting estimators, we introduce a general estimation procedure. We consider modifications and practical issues, and discuss inference, cross validation, and asymptotic theory applying the theoretical framework of Mammen and Nielsen (Biometrika 90: 551–566, 2003). An extensive simulation study shows excellent performance of our method. Furthermore, real data applications from environmetrics and biometrics demonstrate its usefulness.

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

[2]  E. Mammen,et al.  Generalised structured models , 2003 .

[3]  J. M. V. Fernández,et al.  Local polynomial regression smoothers with AR-error structure , 2002 .

[4]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[5]  E. Mammen,et al.  More Efficient Local Polynomial Estimation in Nonparametric Regression With Autocorrelated Errors , 2003 .

[6]  A. Figueiras,et al.  Effect measures in non‐parametric regression with interactions between continuous exposures , 2006, Statistics in medicine.

[7]  Jens Perch Nielsen,et al.  An optimization interpretation of integration and back‐fitting estimators for separable nonparametric models , 1998 .

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

[9]  Stefan Sperlich,et al.  An Adaptive Specification Test For Semiparametric Models , 2007 .

[10]  Jianqing Fan,et al.  Fast Implementations of Nonparametric Curve Estimators , 1994 .

[11]  Enno Mammen,et al.  Smooth backfitting in generalized additive models , 2008, 0803.1922.

[12]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[13]  M. Wand.  Fast Computation of Multivariate Kernel Estimators , 1994 .

[14]  G. Wahba,et al.  Smoothing spline ANOVA for exponential families, with application to the Wisconsin Epidemiological Study of Diabetic Retinopathy : the 1994 Neyman Memorial Lecture , 1995 .

[15]  P. Vieu,et al.  SEMIPARAMETRIC ESTIMATION OF SEPARABLE MODELS WITH POSSIBLY LIMITED DEPENDENT VARIABLES , 2003, Econometric Theory.

[16]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[17]  I. Keilegom,et al.  Estimation of a semiparametric transformation model , 2008, 0804.0719.

[18]  Javier Roca-Pardiñas,et al.  Testing the link when the index is semiparametric - a comparative study , 2007, Comput. Stat. Data Anal..

[19]  Gerhard Tutz,et al.  A comparison of methods for the fitting of generalized additive models , 2008, Stat. Comput..

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

[21]  Javier Roca-Pardiñas,et al.  Predicting binary time series of SO2 using generalized additive models with unknown link function , 2004 .

[22]  Noel A Cressie,et al.  Finding large‐scale spatial trends in massive, global, environmental datasets , 2004 .

[23]  Dag Tjøstheim,et al.  NONPARAMETRIC ADDITIVE MODELS FOR PANELS OF TIME SERIES , 2009, Econometric Theory.

[24]  Wolfgang Härdle,et al.  BOOTSTRAP INFERENCE IN SEMIPARAMETRIC GENERALIZED ADDITIVE MODELS , 2004, Econometric Theory.

[25]  Dag Tjøstheim,et al.  NONPARAMETRIC ESTIMATION AND TESTING OF INTERACTION IN ADDITIVE MODELS , 2002, Econometric Theory.

[26]  S. Wood.  Thin plate regression splines , 2003 .

[27]  C. J. Stone,et al.  Additive Regression and Other Nonparametric Models , 1985 .

[28]  C. J. Stone,et al.  The Dimensionality Reduction Principle for Generalized Additive Models , 1986 .

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

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