  We discuss nonparametric estimation of the distribution function $G(x)$ of
the autoregressive coefficient $a \in (-1,1)$ from a panel of $N$
random-coefficient AR(1) data, each of length $n$, by the empirical
distribution function of lag 1 sample autocorrelations of individual AR(1)
processes. Consistency and asymptotic normality of the empirical distribution
function and a class of kernel density estimators is established under some
regularity conditions on $G(x)$ as $N$ and $n$ increase to infinity. The
Kolmogorov-Smirnov goodness-of-fit test for simple and composite hypotheses of
Beta distributed $a$ is discussed. A simulation study for goodness-of-fit
testing compares the finite-sample performance of our nonparametric estimator
to the performance of its parametric analogue discussed in Beran et al. (2010).
