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- W4379012009 abstract "We introduce projection divergence in the reproducing kernel Hilbert space to test for statistical independence and measure the degree of nonlinear dependence. We suggest a slicing procedure to estimate the kernel projection divergence, which divides a random sample of size n into H slices, each of size c. The entire procedure has the complexity of O(n2), which is prohibitive if n is extremely large. To alleviate computational complexity, we implement this slicing procedure together with a block-wise estimation, which divides the whole sample into B blocks, each of size d. This block-wise and slicing estimation has the complexity of O{n(c+d+logn)}, which reduces the computational complexity substantially if c and d are relatively small. The resultant estimation is asymptotically normal and has the convergence rate of {n(cd)/(c+d)}−1/2. More importantly, this block-wise implementation has the same asymptotic properties as the naive slicing estimation, if c is relatively small, indicating that the block-wise implementation does not result in power loss in independence tests. We demonstrate the computational efficiencies and theoretical properties of this block-wise and slicing estimation through simulations and an application to psychological datasets." @default.
- W4379012009 created "2023-06-02" @default.
- W4379012009 creator A5024232890 @default.
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- W4379012009 date "2023-09-01" @default.
- W4379012009 modified "2023-10-18" @default.
- W4379012009 title "Projection divergence in the reproducing kernel Hilbert space: Asymptotic normality, block-wise and slicing estimation, and computational efficiency" @default.
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- W4379012009 doi "https://doi.org/10.1016/j.jmva.2023.105204" @default.
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