  We consider the CEO problem for non-regular source distributions (such as
uniform or truncated Gaussian). A group of agents observe independently
corrupted versions of data and transmit coded versions over rate-limited links
to a CEO. The CEO then estimates the underlying data based on the received
coded observations. Agents are not allowed to convene before transmitting their
observations. This formulation is motivated by the practical problem of a
firm's CEO estimating (non-regular) beliefs about a sequence of events, before
acting on them. Agents' observations are modeled as jointly distributed with
the underlying data through a given conditional probability density function.
We study the asymptotic behavior of the minimum achievable mean squared error
distortion at the CEO in the limit when the number of agents $L$ and the sum
rate $R$ tend to infinity. We establish a $1/R^2$ convergence of the
distortion, an intermediate regime of performance between the exponential
behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and
the $1/R$ behavior in Gaussian CEO problems [Viswanathan and Berger (1997)].
Achievability is proved by a layered architecture with scalar quantization,
distributed entropy coding, and midrange estimation. The converse is proved
using the Bayesian Chazan-Zakai-Ziv bound.
