Distribution-Free Distribution Regression
نویسندگان
چکیده
‘Distribution regression’ refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y = f(P ) + μ where f is an unknown regression function and μ is a random error. Typically, we do not observe P directly, but rather, we observe a sample from P . In this paper we develop theory and methods for distribution-free versions of distribution regression. This means that we do not make distributional assumptions about the error term μ and covariate P . We prove that when the effective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate.
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