ENH: .interpolate() with EA Dtypes

[jbrockmendel]

ser = pd.Series([1, 2, None, 4], dtype="Int64")

>>> ser.interpolate()
[...]
ValueError: Invalid fill method. Expecting pad (ffill) or backfill (bfill). Got linear

EABackedBlock.interpolate dispatches to EA.fillna, which doesn't handle method="linear". Getting this right probably will require implementing something new at the EA level.

Expected Behavior

pd.Series([1, 2, 3, 4])

[topper-123]

Yeah , I think this should be implemented.

[jbrockmendel]

Just a thought: the logic needed to implement interpolate for arrow ChunkedArray is similar to the logic that would be needed to implement DataFrame.interpolate with axis=1 without transposing.

[jbrockmendel]

@jorisvandenbossche any idea if pyarrow has/plans anything analogous to the numpy/scipy interpolation functions we call from core.missing?