Inference for Spatial Autoregressive Models with Infinite Variance Noises

A self-weighted quantile procedure is proposed to study the inference for a spatial unilateral autoregressive model with independent and identically distributed innovations belonging to the domain of attraction of a stable law with index of stabilityα,α∈(0,2).It is shown that when the model is stationary,the self-weighted quantile estimate of the parameter has a closed form and converges to a normal limiting distribution,which avoids the difficulty of Roknossadati and Zarepour(2010)in deriving their limiting distribution for an M-estimate.On the contrary,we show that when the model is not stationary,the proposed estimates have the same limiting distributions as those of Roknossadati and Zarepour.Furthermore,a Wald test statistic is proposed to consider the test for a linear restriction on the parameter,and it is shown that under a local alternative,the Wald statistic has a non-central chisquared distribution.Simulations and a real data example are also reported to assess the performance of the proposed method.

Post-J test inference in non-nested linear regression models

This paper considers the post-J test inference in non-nested linear regression models. Post-J test inference means that the inference problem is considered by taking the first stage J test into account. We first propose a post-J test estimator and derive its asymptotic distribution. We then consider the test problem of the unknown parameters, and a Wald statistic based on the post-J test estimator is proposed. A simulation study shows that the proposed Wald statistic works perfectly as well as the two-stage test from the view of the empirical size and power in large-sample cases, and when the sample size is small, it is even better. As a result,the new Wald statistic can be used directly to test the hypotheses on the unknown parameters in non-nested linear regression models.