Question

How is the Cepheid yardstick validated?

Answer 1

For relatively close stars there is one method that works.

Explanation:

Parallax measurements (the apparent movement of the target star against a very distant background of other objects) due to the rotation of the earth around the sun allows us an independent measure of distance.

Wikipedia can help with the geometry of this and has better diagrams than I can produce.

Other distance scales also work, but it is less secure as we move outwards (assumptions are compounded)