Regarding Assumptions

[startz]

If the observations are ordered so that the model is equivalent to a lagged dependent variable model in the time dimension then EViews AR(1) command will provide a valid MLE. More generally, the clip you posted ends with saying various methods are "reviewed below." "Below" might be the best thing to read.

[jiya]

my problem is not estimating the model in eviews.....rather i am looking for justification of using MLE in "spatial lag model"!!!! How does MLE provide efficient estimator in case of spatial lag model.??

[startz]

It is possible to write out the likelihood function such that the problematic correlations are factored out. That's the usual procedure for dealing with lag dependent variables in the presence of serial correlation. In the usual time dimension framework, this is called quasi-differencing. I'm not sure what it's called in the spatial framework.

[jiya]

would you take the trouble to write down that expression here??

[startz]

would you take the trouble to write down that expression here??

A) The expression is standard; it's in most introductory econometrics texts.
B) You have posted an excerpt that says it gives a full explanation.

Why don't you take a look at a textbook or at the material you excerpted, and then if you get stuck come back and tell us what part you don't understand.