  In this paper, some of the properties of non-parametric estimation of the
expectation of g(X) (any function of X), by using a Judgment
Post-stratification Sample (JPS), are discussed. A class of estimators
(including the standard JPS estimator and a JPS estimator proposed by Frey and
Feeman (2012, Comput. Stat. Data An.)) is considered. The paper provides mean
and variance of the members of this class, and examines their consistency and
asymptotic distribution. Specifically, the results are for the estimation of
population mean, population variance and CDF. We show that any estimators of
the class may be less efficient than Simple Random Sampling (SRS) estimator for
small sample sizes. We prove that the relative efficiency of some estimators in
the class with respect to Balanced Ranked Set Sampling (BRSS) estimator tends
to 1 as the sample size goes to infinity. Furthermore, the standard JPS mean
estimator and, Frey and Feeman JPS mean estimator are specifically studied and
we show that two estimator have the same asymptotic distribution. For the
standard JPS mean estimator, in perfect ranking situations, optimum values of H
(the ranking class size), for different sample sizes, are determined
non-parametrically for populations that are not heavily skewed or thick tailed.
We show that the standard JPS mean estimator may be more efficient than BRSS
for large sample sizes, in situations in which we can use a larger class size
for H in JPS set-up.
