When I use focal statistics setting the neighborhood of each processing cell to be a circle with 800m radius (map units, not number of cells), how are the statistics calculated in the edges of my region, when in that radius there are ΝoData pixels? In my case, I have selected for each neighborhood to be defined by a circle with 800m radius around each processing pixel. What I get in the edges is something like a "buffer" around my region that equals to the circle radius. Is this normal? How is it explained?
Since this is software specific, you should tag this as ArcGIS.
Software help is your friend. If you look at the usage of FocalStatistics you will see that there is an argument "ignore_nodata" that controls exactly what you are observing.
ignore_nodata - Denotes whether NoData values are ignored by the statistic calculation.
DATA — Specifies that if a NoData value exists within a neighborhood, the NoData value will be ignored. Only cells within the neighborhood that have data values will be used in determining the output value. This is the default.
NODATA —Specifies that if any cell in a neighborhood has a value of NoData, the output for the processing cell will be NoData. With this option, the presence of a NoData value implies that there is insufficient information to determine the statistic value for the neighborhood.