I have samples from a $d$ dimensional distribution $p$. The distribution of $p$ is unknown. I want to use the samples to judge whether or not the $p$ is close to a standard unit Gaussian distribution. I believe there should be some standard approaches for this question, but unfortunately, I do not find a solution for high-dimensional cases. BY high dimensional, I mean $d$ is several thousand.
The only approach in my mind is doing one dimension testing with projecting data to low dimension.