How to get PyPI to automatically install dependencies

This is an unfortunate (and known) downside to TestPyPI: The issue is that sklearn does not exist on TestPyPI, and by installing your package from there, you are telling pip to look for dependencies there as well.

Instead, you should publish to PyPI instead, and use a pre-release version so as not to pollute your versions. You can delete these pre-releases from the project later.

I realized that installing packages from test.PyPI does not install all packages, since some of these packages are hosted on PyPI and not test.PyPI.

When I published the package on PyPI as a pre-release version (1.0a1), instead on test.PyPI, the dependencies were correctly installed. Hence, the problem was purely with test.PyPI.

You can specify multiple indexes via --extra-index-url. Point it to TestPyPI so your package is pulled from there, the deps from PyPI:

$ pip install myPackage --extra-index-url=https://test.pypi.org/simple/

However, the real root for the issue is that you have included the wrong dist name for the scikit-learn package. Replace sklearn with scikit-learn:

setup(
    ...,
    install_requires=['numpy', 'pandas', 'scikit-learn'],
)