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vnmabus / dcor

Distance correlation and related E-statistics in Python
https://dcor.readthedocs.io
MIT License
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Can distance correlation-based t test is theoretically correct to implement for "uni"-dimensional data? #52

Closed Palash123-4 closed 1 year ago

Palash123-4 commented 1 year ago

The whole t-test is based on the idea that the dimensions of X and Y must be high. What do you think about that?

vnmabus commented 1 year ago

Yes, that is true. It is mentioned in the docstring:

"Test of independence for high dimension."

Moreover, the example also expands on that:

"The test illustrated here is an asymptotic test, that relies in the approximation of the statistic distribution to the Student’s t-distribution under the null hypothesis, when the dimension of the data goes to infinity. This test is thus faster than permutation tests, as it does not require the use of permutations of the data, and it is also deterministic for a given dataset. However, the test should be applied only for high-dimensional data, at least in theory."

Palash123-4 commented 1 year ago

Thanks for your response. Luckily, I found a univariate version test also based on distance correlation in "https://www.tandfonline.com/doi/epdf/10.1080/10618600.2021.1938585?needAccess=true&role=button".