A CONSISTENT TEST OF CONDITIONAL PARAMETRIC DISTRIBUTIONS

This paper proposes a new nonparametric test for conditional parametric distribution functions based on the first-order linear expansion of the Kullback–Leibler information function and the kernel estimation of the underlying distributions. The test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric distribution is correctly specified, whereas asymptotically rejecting the null with probability one if the parametric distribution is misspecified. The test is also shown to have power against any local alternatives approaching the null at rates slower than the parametric rate n−1/2. The finite sample performance of the test is evaluated via a Monte Carlo simulation.

[1]  Adonis Yatchew,et al.  Nonparametric Regression Tests Based on Least Squares , 1992, Econometric Theory.

[2]  P. Hall.  Central limit theorem for integrated square error of multivariate nonparametric density estimators , 1984 .

[3]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

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

[5]  Quang Vuong,et al.  NONPARAMETRIC SIGNIFICANCE TESTING , 2000, Econometric Theory.

[6]  Yanqin Fan.  Testing the Goodness of Fit of a Parametric Density Function by Kernel Method , 1994, Econometric Theory.

[7]  D. Darling.  The Kolmogorov-Smirnov, Cramer-von Mises Tests , 1957 .

[8]  Donald W. K. Andrews,et al.  A Conditional Kolmogorov Test , 1997 .

[9]  P. Robinson.  Consistent Nonparametric Entropy-Based Testing , 1991 .

[10]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[11]  Yoon-Jae Whang,et al.  Tests of specification for parametric and semiparametric models , 1993 .

[12]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

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

[14]  A Consistent Test for Linearity in Partially Linear Regression Models , 1994 .

[15]  Yongmiao Hong,et al.  Consistent Specification Testing via Nonparametric Series Regression , 1995 .

[16]  Maxwell B. Stinchcombe,et al.  CONSISTENT SPECIFICATION TESTING WITH NUISANCE PARAMETERS PRESENT ONLY UNDER THE ALTERNATIVE , 1998, Econometric Theory.

[17]  Thomas M. Stoker,et al.  Semiparametric Estimation of Index Coefficients , 1989 .

[18]  Jeffrey M. Wooldridge,et al.  A Test for Functional Form Against Nonparametric Alternatives , 1992, Econometric Theory.

[19]  Prakasa Rao.  Nonparametric functional estimation , 1983 .

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

[21]  Herman J. Bierens,et al.  A consistent conditional moment test of functional form , 1990 .