For testing lack of correlation against spatial autoregressive alternatives, Lagrange multiplier tests enjoy their usual computational advantages, but the (χ2) first-order asymptotic approximation to critical values can be poor in small samples. We develop refined tests for lack of spatial...

For testing lack of correlation against spatial autoregressive alternatives, Lagrange multiplier tests enjoy their usual computational advantages, but the (χ-super-2) first‐order asymptotic approximation to critical values can be poor in small samples. We develop refined tests for lack of...

We consider testing the null hypothesis of no spatial autocorrelation against the alternative of first order spatial autoregression. A Wald test statistic has good first order asymptotic properties, but these may not be relevant in small or moderate-sized samples, especially as (depending on...