A small, complete example of the issue

>>> import pandas as pd
>>> pd.Series(index=[3,2,1,4,3]).sort_index(kind='mergesort')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: sort_index() got an unexpected keyword argument 'kind'

Expected Output

A Series sorted by the index, i.e.:

>>> pd.Series(index=[3,2,1,4,3]).sort_index()
1   NaN
2   NaN
3   NaN
3   NaN
4   NaN
dtype: float64

Output of pd.show_versions()

## INSTALLED VERSIONS commit: None python: 2.7.6.final.0 python-bits: 64 OS: Linux OS-release: 4.4.0-42-generic machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: en_US.UTF-8 pandas: 0.18.1 nose: 1.3.1 pip: 1.5.4 setuptools: 3.3 Cython: 0.20.1post0 numpy: 1.11.0 scipy: 0.13.3 statsmodels: None xarray: None IPython: 1.2.1 sphinx: 1.2.2 patsy: None dateutil: 2.5.3 pytz: 2016.4 blosc: None bottleneck: None tables: None numexpr: None matplotlib: 1.3.1 openpyxl: None xlrd: None xlwt: None xlsxwriter: 0.8.7 lxml: None bs4: 4.4.1 html5lib: 0.999 httplib2: 0.8 apiclient: None sqlalchemy: None pymysql: None psycopg2: None jinja2: 2.7.2 boto: None pandas_datareader: None

Comment From: brandonmburroughs

It looks like we use _nargsort in DataFrame (relevant code), but sort_values in Series (relevant code). We can update sort_index in Series to follow the same pattern.

Comment From: jreback

a dupe of #13589