Robust tests in semiparametric partly linear models

This paper focuses on the problem of testing the null hypothesis H0β: β = βo and H0g: g = go, under a semiparametric partly linear regression model yi = x′iβ + g(ti) + i, 1 ≤ i ≤ n by using a three–step robust estimate for the regression parameter and the regression function. Two families of tests statistics are considered for H0β: β = βo and their asymptotic distributions are studied under the null hypothesis and under contiguous alternatives. A statistic is introduced to test the nonparametric component which turns out to behave more resistantly than the classical one. A Monte Carlo study is performed to compare the finite sample behavior of the proposed tests with the classical one. Key words: hypothesis testing, partly linear models, robust estimation, smoothing tech-niques. ∗This research was partially supported by Grants pict # 03-00000-006277 from anpcyt, X-094 fro