API: add infer_objects for soft conversions
 - [x] closes #11221  (more or less)
 - [ ] tests added / passed
 - [x] passes ``git diff upstream/master --name-only -- '*.py' | flake8 --diff`` (On Windows, ``git diff upstream/master -u -- "*.py" | flake8 --diff`` might work as an alternative.)
 - [x] whatsnew entry

Need to add more tests cases still
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=h1) Report
> Merging [#16915](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/4ca9fcd73225af9cb1dc2acc99bb494dc5f8926a?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/16915/graphs/tree.svg?token=eZ4WkYLtcO&src=pr&width=650&height=150)](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #16915      +/-   ##
==========================================
- Coverage   90.99%   90.97%   -0.02%     
==========================================
  Files         161      161              
  Lines       49303    49294       -9     
==========================================
- Hits        44863    44846      -17     
- Misses       4440     4448       +8
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `88.74% <100%> (-0.01%)` | :arrow_down: |
| #single | `40.18% <33.33%> (-0.07%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/generic.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ2VuZXJpYy5weQ==) | `92.31% <100%> (+0.01%)` | :arrow_up: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/plotting/\_converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19jb252ZXJ0ZXIucHk=) | `63.23% <0%> (-1.82%)` | :arrow_down: |
| [pandas/compat/\_\_init\_\_.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL2NvbXBhdC9fX2luaXRfXy5weQ==) | `60.67% <0%> (-1.55%)` | :arrow_down: |
| [pandas/core/config\_init.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29uZmlnX2luaXQucHk=) | `95.86% <0%> (-0.1%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.76% <0%> (-0.05%)` | :arrow_down: |
| [pandas/core/sparse/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc3BhcnNlL2ZyYW1lLnB5) | `94.24% <0%> (-0.02%)` | :arrow_down: |
| [pandas/core/dtypes/cast.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZHR5cGVzL2Nhc3QucHk=) | `86.89% <0%> (ø)` | :arrow_up: |
| [pandas/core/panel.py](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcGFuZWwucHk=) | `96.94% <0%> (ø)` | :arrow_up: |
| ... and [6 more](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=footer). Last update [4ca9fcd...4268007](https://codecov.io/gh/pandas-dev/pandas/pull/16915?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 thanks @gfyoung @jreback @bashtage  @chris-b1 when you have a chance: http://pandas-docs.github.io/pandas-docs-travis/whatsnew.html#infer-objects-type-conversion

``.dtype`` -> ``.dtypes``

I don't know why ``:meth:`` doesn't work, I use ``:func:`` which seems to....