  Nonlinear combinations of direct observables are often used to estimate
quantities of theoretical interest. Without sufficient caution, this could lead
to biased estimations. An example of great interest is the skewness $S_3$ of
the galaxy distribution, defined as the ratio of the third moment $\xibar_3$
and the variance squared $\xibar_2^2$. Suppose one is given unbiased estimators
for $\xibar_3$ and $\xibar_2^2$ respectively, taking a ratio of the two does
not necessarily result in an unbiased estimator of $S_3$. Exactly such an
estimation-bias affects most existing measurements of $S_3$. Furthermore,
common estimators for $\xibar_3$ and $\xibar_2$ suffer also from this kind of
estimation-bias themselves: for $\xibar_2$, it is equivalent to what is
commonly known as the integral constraint. We present a unifying treatment
allowing all these estimation-biases to be calculated analytically. They are in
general negative, and decrease in significance as the survey volume increases,
for a given smoothing scale. We present a re-analysis of some existing
measurements of the variance and skewness and show that most of the well-known
systematic discrepancies between surveys with similar selection criteria, but
different sizes, can be attributed to the volume-dependent estimation-biases.
This affects the inference of the galaxy-bias(es) from these surveys. Our
methodology can be adapted to measurements of analogous quantities in quasar
spectra and weak-lensing maps. We suggest methods to reduce the above
estimation-biases, and point out other examples in LSS studies which might
suffer from the same type of a nonlinear-estimation-bias.
