Testing the link when the index is semiparametric - a comparative study

Generalized structured models are popular in applied statistics. They can circumvent the curse of dimensionality and provide results that are easy to interpret. However, there are two major concerns that need to be addressed before they are applied. Firstly, the credibility of the specified structure, such as additivity, and secondly, the specification of the link function need to be assessed. The focus is on the latter issue. In many cases it is feasible to estimate a nonparametric link, but the effort is often not justified. In contrast parametric links enable the use of likelihood-based estimates, which are asymptotically efficient, and which perform excellently in practice, particularly for small samples. Several statistics for testing the credibility of parametric link specifications are introduced. Estimation and implementation are discussed, and the performance of the statistics is compared in an intensive simulation study. Applications to real data are also described.

[1]  Joel L. Horowitz,et al.  NONPARAMETRIC ESTIMATION OF A GENERALIZED ADDITIVE MODEL WITH AN UNKNOWN LINK FUNCTION , 2001 .

[2]  G. Lugosi,et al.  Goodness‐of‐fit Tests Based on the Kernel Density Estimator , 2005 .

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

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

[5]  Winfried Stute,et al.  Nonparametric model checks for regression , 1997 .

[6]  Herman J. Bierens,et al.  Asymptotic Theory of Integrated Conditional Moment Tests , 1997 .

[7]  Javier Roca-Pardiñas,et al.  Testing for interactions in generalized additive models: Application to SO2 pollution data , 2005, Stat. Comput..

[8]  László Györfi,et al.  On the asymptotic properties of a nonparametric L/sub 1/-test statistic of homogeneity , 2005, IEEE Transactions on Information Theory.

[9]  Oliver Linton,et al.  Testing additivity in generalized nonparametric regression models with estimated parameters , 2001 .

[10]  W. Härdle,et al.  Direct Semiparametric Estimation of Single-Index Models with Discrete Covariates dpsfb950075.ps.tar = Enno MAMMEN J.S. MARRON: Mass Recentered Kernel Smoothers , 1996 .

[11]  E. Mammen,et al.  Comparing Nonparametric Versus Parametric Regression Fits , 1993 .

[12]  Yanqin Fan,et al.  Consistent model specification tests : Omitted variables and semiparametric functional forms , 1996 .

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

[14]  Javier Roca-Pardiñas,et al.  Non‐parametric estimation of the odds ratios for continuous exposures using generalized additive models with an unknown link function , 2005, Statistics in medicine.

[15]  W. Härdle,et al.  Semiparametric Single Index Versus Fixed Link Function Modelling , 1997 .

[16]  W. González-Manteiga,et al.  Testing the hypothesis of a general linear model using nonparametric regression estimation , 1993 .

[17]  A bootstrap test for single index models , 2001 .

[18]  Oliver Linton,et al.  A nonparametric test of additivity in generalized nonparametric regression with estimated parameters , 2001 .

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

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

[21]  Winfried Stute,et al.  Bootstrap Approximations in Model Checks for Regression , 1998 .

[22]  Ker-Chau Li,et al.  Regression Analysis Under Link Violation , 1989 .

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