Robust tests of inequality constraints and one-sided hypotheses in the linear model

For the linear regression model with independent and identically distributed errors, robust tests of various hypotheses on the regression parameter are developed; by ‘robust’, we mean robustness of size and power against long-tailed error distributions which may not be symmetric. The proposed test statistic, denoted by FM, resembles the usual F-statistic. The two main results are (i) under the null hypothesis, the asymptotic distribution of FM and that of the least squares based F-statistic are the same; and (ii) the Pitman asymptotic efficiency of FM relative to F is equal to the asymptotic efficiency of the corresponding M-estimator relative to the least squares estimator. An example and simulation results illustrate that FM has desirable robustness properties compared to F