A consistent test for heteroscedasticity in semi-parametric regression with nonparametric variance function based on the kernel method

It is important to detect the variance heterogeneity in regression models. Heteroscedasticity tests have been well studied in parametric and nonparametric regression models. This paper presents a consistent test for heteroscedasticity for nonlinear semi-parametric regression models with nonparametric variance function based on the kernel method. The properties of the test are investigated through Monte Carlo simulations. The test methods are illustrated with a real example.

[1]  Bo-Cheng Wei,et al.  Testing for Heteroscedasticity in Nonlinear Regression Models , 2003 .

[2]  S. Weisberg,et al.  Diagnostics for heteroscedasticity in regression , 1983 .

[3]  C. Dean.  Testing for Overdispersion in Poisson and Binomial Regression Models , 1992 .

[4]  R. L. Eubank,et al.  Detecting Heteroscedasticity in Nonparametric Regression , 1993 .

[5]  Hans-Georg Müller,et al.  On a Semiparametric Variance Function Model and a Test for Heteroscedasticity , 1995 .

[6]  J. Rice.  Bandwidth Choice for Nonparametric Regression , 1984 .

[7]  Chih-Ling Tsai,et al.  Score test for the first-order autoregressive model with heteroscedasticity , 1986 .

[8]  Adrian Bowman,et al.  Testing for constant variance in a linear model , 1997 .

[9]  Daniel F. Heitjan,et al.  Testing and Adjusting for Departures from Nominal Dispersion in Generalized Linear Models , 1993 .

[10]  Holger Dette,et al.  A new test for the parametric form of the variance function in non‐parametric regression , 2007 .

[11]  J. Sacks,et al.  Designs for Regression Problems with Correlated Errors III , 1966 .

[12]  Holger Dette,et al.  Testing heteroscedasticity in nonparametric regression , 1998 .

[13]  Yong Li,et al.  Testing for departures from nominal dispersion in generalized nonlinear models with varying dispersion and/or additive random effects , 2008 .

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

[15]  Holger Dette,et al.  A consistent test for heteroscedasticity in nonparametric regression based on the kernel method , 2002 .

[16]  Holger Dette,et al.  A simple test for the parametric form of the variance function in nonparametric regression , 2009 .

[17]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[18]  Jinhong You,et al.  Testing heteroscedasticity in partially linear regression models , 2005 .

[19]  J. Witmer,et al.  Nonlinear Regression Modeling. , 1984 .

[20]  W. Fung,et al.  Testing for Varying Dispersion in Exponential Family Nonlinear Models , 1998 .

[21]  Lisa M. Ganio,et al.  Diagnostics for Overdispersion , 1992 .

[22]  Jeffrey S. Simonoff,et al.  Use of Modified Profile Likelihood for Improved Tests of Constancy of Variance in Regression , 1994 .

[23]  Lixing Zhu,et al.  Heteroscedasticity diagnostics for t linear regression models , 2009 .

[24]  Hannelore Liero,et al.  Testing homoscedasticity in nonparametric regression , 2003 .

[25]  Holger Dette,et al.  A test for the parametric form of the variance function in apartial linear regression model , 2007 .

[26]  Juan M. Vilar-Fernández,et al.  Two tests for heteroscedasticity in nonparametric regression , 2009, Comput. Stat..

[27]  B. Wei,et al.  Varying Dispersion Diagnostics for Inverse Gaussian Regression Models , 2004 .

[28]  J. Zheng,et al.  A consistent test of functional form via nonparametric estimation techniques , 1996 .