Abstract
What do you do if you believe (or someone tells you) that the conditional distributions of X given Y = 0 and Y = 1 are members of a given family of distributions, described by finitely many real-valued parameters? Of course, it does not make sense to say that there are, say, six parameters. By interleaving the bits of binary expansions, we can always make one parameter out of six, and by splitting binary expressions, we may make a countable number of parameters out of one parameter (by writing the bits down in triangular fashion as shown below).
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© 1996 Springer Science+Business Media New York
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Devroye, L., Györfi, L., Lugosi, G. (1996). Parametric Classification. In: A Probabilistic Theory of Pattern Recognition. Stochastic Modelling and Applied Probability, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0711-5_16
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DOI: https://doi.org/10.1007/978-1-4612-0711-5_16
Publisher Name: Springer, New York, NY
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