  Unevenly spaced time series are common in astronomy because of the day-night
cycle, weather conditions, dependence on the source position in the sky,
allocated telescope time, corrupt measurements, for example, or be inherent to
the scanning law of satellites like Hipparcos and the forthcoming Gaia.
Irregular sampling often causes clumps of measurements and gaps with no data
which can severely disrupt the values of estimators. This paper aims at
improving the accuracy of common statistical parameters when linear
interpolation (in time or phase) can be considered an acceptable approximation
of a deterministic signal. A pragmatic solution is formulated in terms of a
simple weighting scheme, adapting to the sampling density and noise level,
applicable to large data volumes at minimal computational cost. Tests on time
series from the Hipparcos periodic catalogue led to significant improvements in
the overall accuracy and precision of the estimators with respect to the
unweighted counterparts and those weighted by inverse-squared uncertainties.
Automated classification procedures employing statistical parameters weighted
by the suggested scheme confirmed the benefits of the improved input
attributes. The classification of eclipsing binaries, Mira, RR Lyrae, Delta
Cephei and Alpha2 Canum Venaticorum stars employing exclusively weighted
descriptive statistics achieved an overall accuracy of 92 per cent, about 6 per
cent higher than with unweighted estimators.
