Stochastically weighted average conditional moment tests of functional form. (English) Zbl 1506.62509
Summary: We develop a new consistent conditional moment test of functional form based on nuisance parameter indexed sample moments first presented in [H. J. Bierens, J. Econom. 20, 105–134 (1982; Zbl 0549.62076); with W. Ploberger, Econometrica 65, No. 5, 1129–1151 (1997; Zbl 0927.62085)]. We reduce the nuisance parameter space to known countable sets, which leads to a weighted average conditional moment test in the spirit of Bierens and Ploberger’s integrated conditional moment test (ICM). The weights are possibly stochastic in an arbitrary way, integer-indexed and flexible enough to cover a range of tests from average to higher quantile to maximum tests. The limit distribution under the null and local alternative belong to the same class as the ICM statistic, hence our test is admissible if the errors are Gaussian, and a flat weight leads to the greatest weighted average local power.
MSC:
| 62P20 | Applications of statistics to economics |
| 62J02 | General nonlinear regression |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
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