Diaconis, P.; Freedman, D. A. Nonparametric binary regression: A Bayesian approach. (English) Zbl 0797.62031 Ann. Stat. 21, No. 4, 2108-2137 (1993). Let be given a binary random variable \(\eta\) depending on a whole sequence of binary covariates \(\xi = (\xi_ k)\) and define \(f(\xi): = P(\eta = 1 \mid \xi)\) which can be considered as a function mapping [0,1] into itself. Let be given \(2^ n\) data with independent \(\eta_ k\) having covariates covering all possible patterns of the first \(n\) covariates, the remaining covariates are assumed to be uniform and independent.Defining a prior distribution \(\sum^ \infty_{k=1} \pi_ kw_ k/ \sum w_ \nu\) where \(\pi_ k\) is uniform on the set of functions \(f\) which depend on the first \(k\) covariates only and \(w_ k>0\) for infinitely many \(k\) are weights for the dimensions, the authors discuss the consistency of the Bayes estimates for \(f\). If the weights \(w_ k\) are decreasing rapidly enough there is consistency, otherwise the function \(f \equiv 1/2\) is not estimated consistently. In any case, if \(f\) depends only on finitely many covariates the corresponding order can be estimated consistently. Although the model is very specific this is an interesting paper. Reviewer: U.Stadtmüller (Ulm) Cited in 10 Documents MSC: 62G07 Density estimation 62A01 Foundations and philosophical topics in statistics 62G05 Nonparametric estimation 62E20 Asymptotic distribution theory in statistics Keywords:binary regression; model selection; binary random variable; sequence of binary covariates; prior distribution; consistency; Bayes estimates PDFBibTeX XMLCite \textit{P. Diaconis} and \textit{D. A. Freedman}, Ann. Stat. 21, No. 4, 2108--2137 (1993; Zbl 0797.62031) Full Text: DOI