There is a 10 meter resolution land cover raster. An analyst wishes to resample 10 meter raster to 30 meter raster. The analyst selects the Bilinear Resampling technique in the `Resample`

tool of the Raster Processing toolset of ArcGIS 10.3.

ArcGIS 10.3 help defines the Bilinear Resampling technique as:

Performs a bilinear interpolation and determines the new value of a cell based on a weighted distance average of the four nearest input cell centers. It is useful for continuous data and will cause some smoothing of the data.

A 30 meter output cell will contain nine cells from the input 10 meter raster. The closest input cell center will be the one that perfectly overlaps the output cell center. That leaves three remaining input cell center values for inclusion in the bilinear interpolation. In the resample of 10 m to 30 m there are eight remaining values that are equidistant to the output cell center.

Which 3 values of the 8 equidistant values are utilized to create the output?

Sample—Help | ArcGIS Desktop

Which is why it is sometimes better use rolling statistics and your own kernel.

I have covered this in a couple of blog posts as well

Aggregation of raster data

Generalization tools for rasters...