Consistent Specification Testing via Nonparametric Series Regression

This paper proposes two consistent one-sided specification tests for parametric regression models, one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values; the other based on the difference in sums of squared residuals between the parametric and nonparametric models. The authors estimate the nonparametric model by series regression. The new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate [square root of] n under misspecification, while avoiding weighting, sample splitting, and nonnested testing procedures used elsewhere. Copyright 1995 by The Econometric Society.

[1]  Alberto Holly,et al.  A Remark on Hausman's Specification Test , 1982 .

[2]  H. Bierens,et al.  On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity , 1994, Econometric Theory.

[3]  A. Ronald Gallant,et al.  On the asymptotic normality of Fourier flexible form estimates , 1991 .

[4]  P. Gozalo,et al.  A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models , 1993, Econometric Theory.

[5]  Paul L. Speckman,et al.  Curve fitting by polynomial-trigonometric regression , 1990 .

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

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

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

[9]  D. Andrews.  Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models , 1991 .

[10]  Peter F. de Jong,et al.  A central limit theorem for generalized quadratic forms , 1987 .

[11]  J. Hausman.  Specification tests in econometrics , 1978 .

[12]  A. Gallant,et al.  Unbiased determination of production technologies , 1982 .

[13]  Dale W. Jorgenson,et al.  Statistical inference for a system of simultaneous, non-linear, implicit equations in the context of instrumental variable estimation , 1979 .

[14]  Bodhini R. Jayasuriya,et al.  Testing for Polynomial Regression Using Nonparametric Regression Techniques , 1996 .

[15]  D. Andrews.  Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables , 1988, Econometric Theory.

[16]  H. Bierens.  Consistent model specification tests , 1982 .