  In this paper, the model $Y_i=g(Z_i),\ i=1,2,...,n$ with $Z_i$ being random
variables with known distribution and $g(x)$ being unknown strictly increasing
function is proposed and almost sure convergence of estimator for $g(x)$ is
proved for i.i.d and short range dependent data. Confidence intervals and bands
are constructed for i.i.d data theoretically and confidence intervals are
introduced for short range dependent data through resampling. Besides, a test
for equivalence of $g(x)$ to the desired function is proposed. Finite sample
analysis and application of this model on an urban waste water treatment
plant's data is demonstrated as well.
