I am trying to wrap my head around the original wavelet shrinkage papers of Donoho and others from the mid-90s. There are a couple of curious things that confuse me, and I'd appreciate some input:

  • The universal threshold is often (and also in secondary literature) given as $\sigma\sqrt{2\ln n}$, but sometimes I see $\frac{\sigma}{\sqrt{n}}\sqrt{2\ln n}$, e.g. in "Wavelet Shrinkage: Asymptopia?". The latter seems utterly wrong...
  • The minimax threshold $\lambda^\star_n$ as defined in "Ideal spatial adaptation by wavelet shrinkage" has the property that $(\lambda^\star_n)^2 = 2\ln(n+1) - 4\ln(\ln(n +1)) - \ln 2\pi + o(1)$. I've tried to use the square root of this to derive values for $\lambda^\star_n$ (ignoring the $o(1)$, guess that's what's causing my problem?), however, they are very different from the ones in table 2. Is there an explicit formula or algorithm for $\lambda^\star_n$?

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