The test of normality for resiuals of a neural network

I have used Lillifores test to examine the normality of residuals of a neural netwoek.The result showed that the residuals of my ANN is not normally distributed what does it mean?

[dpb]

That the model residuals aren't normally distributed. Not much, really other than that statistics computed from them relying on such an assumption aren't reliable, but otherwise, probably nothing.

[Greg Heath]

The above comment should probably be upgraded to an ANSWER.

Greg

[Rita]

Thanks dpb,Greg.

Answer 1

[Greg Heath]

Original comment by dpb on 30 Sep 2016 at 20:38 upgraded to an ANSWER:

That the model residuals aren't normally distributed. Not much, really other than that statistics computed from them relying on such an assumption aren't reliable, but otherwise, probably nothing.

[Rita]

Thanks Greg,I would really appreciate if you could send a reference( an article or ...) for the answer which shows that the residual of ANN does not follow a normal distribution but still the ANN predicts well.

[dpb]

Well, since I was the one who actually crafted the answer (Greg simply moved my comment to an answer as well as agreeing) I'll not leave the onus on him to defend it.

In short, I have no specific reference, only that estimation itslef is NOT reliant upon the underlying distribution; only that assumptions regarding error distributions and the statistics associated with them are, for the most part, based on the assumption of normality. This isn't anything particularly to do about "normality" being something magic, only that it is one of the few distributions for which analytic solutions are possible from which to write the necessary test statistic properties to be able to thus compute confidence intervals and the like.

If the residuals aren't normal, then those statistics aren't necessarily accurate and if those kinds of estimates are important then you're forced to try to other techniques to evaluate those parameters.

But, that doesn't say anything at all about the actual ability of the model to predict results; only actual looking at the magnitude of the residuals themselves and how it performs for new predictions when data become available to confirm/deny its accuracy can tell you how well (or poorly) it actual performs as a model.

That said, just how nonnormal are the results? Unless they're exceedingly skewed or much broader-tailed than a normal, the magnitude of the deviation is probably not going to make a great deal of difference.