Several statistics have been proposed for measuring the kinetic Sunyaev-Zeldovich (kSZ) effect by combining the small-scale CMB with galaxy surveys. We review five such statistics, and show that they are all mathematically equivalent to the optimal bispectrum estimator of type $⟨ggT⟩$. Reinterpreting these kSZ statistics as special cases of bispectrum estimation makes many aspects transparent, for example optimally weighting the estimator or incorporating photometric redshift errors. We analyze the information content of the bispectrum and show that there are two observables: the small-scale galaxy-electron power spectrum $P_{ge}(k_S)$, and the large-scale galaxy-velocity power spectrum $P_{gv}(k)$. The cosmological constraining power of the kSZ effect arises from its sensitivity to fluctuations on large length scales, where its effective noise level can be much better than galaxy surveys.

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• Cosmic microwave background
• Cosmological parameters
• Large scale structure of the Universe