Abstract
Traditionally, Rao's score (RS) tests are constructed under a parametric specification of the probability density function. We estimate the density function by a non-parametric estimator and consider a semi-parametric Rao's score (SPRS) test for a set of hypotheses concerning the parametric model. The asymptotic distribution of the SPRS test is analyzed. Further, for the regression model, we carry out a set of Monte Carlo experiments to analyze the size and power of the SPRS test in small samples. The robustness of SPRS test to the choice of the density estimator is also analyzed.
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