The non-parametric interval estimator for the analysis of environmental data

Abstract

Data treatment is the routine procedure to get valuable infonnation on environmental
processes. The simple statistical estimations, both parametrical and non-parametrical, are
widely used in practice to evaluate parameters that characterize the quality of different
environmental compounds. The interval estimations ( confidence interval) are especially
useful for making inferences. The actual problem is in that if intrinsic distribution is unknown
and sample size is low then there is no suitable method for reliable interval estimations of
parameters.
The non-parametric method for the interval estimations of environmental parameters is
offered based on Monte-Carlo procedure. It does not impose any limits on the sample size or
sample distribution. Instead, it is supposed that minimum and maximum values of the
population are known. This approach looks like bootstrapping that uses the Monte-Carlo
procedure but unlike it enables to obtain the improved confidence interval, even for the small
size sample. Monte-Carlo algorithm includes statistical trials that are carried out with two
piece-wise linear approximations of the integral that represents the evaluated parameter. The
Monte-Carlo method also enables to restore the thin structure of a posteriori probability
distribution of estimated parameter for the small size sample.
The properties of the proposed Monte-Carlo method are compared with those of the
bootstrapping. Some examples of application to the problems of hydrological parameter
assessments are also presented and specific conditions of it application are discussed.