NONPARAMETRIC BINARY REGRESSION WITH RANDOM COVARIATES
P. Diaconis D. Freedman
Abstract: The performance of Bayes’ estimates is studied under an assumption of
conditional exchangeability. More exactly, for each subject in a data set, let
be a vector of binary covariates and let be a binary response variable with
Here, is an unknown function, to be estimated from the data; the
subjects are independent, and the ’s are iid uniform. Define a prior distribution on as
where is uniform on the set of which only depend on the first
covariates and for infinitely many Bayes’ estimates are consistent at all if
decreases rapidly as increase. Otherwise, the estimates are inconsistent at
be a vector of binary covariates and let 
be a binary response variable with
Here, 
is an unknown function, to be estimated from the data; the
subjects are independent, and the 
’s are iid uniform. Define a prior distribution on 
as
where 
is uniform on the set of 
which only depend on the first 
covariates and 
for infinitely many 
Bayes’ estimates are consistent at all 
if
decreases rapidly as 
increase. Otherwise, the estimates are inconsistent at 