Lanzante, J. R., 1996: Resistant, robust & non-parametric techniques for the analysis of climate data: Theory and examples, including applications to historical radiosonde station data. International Journal of Climatology, 16(11), 1197-1226.
Abstract: Basic traditional parametric statistical techniques
are used widely in climatic studies for characterizing the level (central
tendency) and variability of variables, assessing linear relationships
(including trends), detection of climate change, quality control and assessment,
identification of extreme events, etc. These techniques may involve estimation
of parameters such as the mean ( a measure of location), variance (a measure
of scale) and correlation/regression coefficients (measures of linear association);
in addition, it is often desirable to estimate the statistical significance
of the difference between estimates of the mean from two different samples
as well as the significance of estimated measures of association. The validity
of these estimates is based on underlying assumptions that sometimes are
not met by real climate data. Two of these assumptions are addressed here:
normality and homogeneity (and as a special case statistical stationarity);
in particular, contamination from a relatively few 'outlying values' may
greatly distort the estimates. Sometimes these common techniques are used
in order to identify outliers; ironically they may fail because of the
presence of the outliers!
Alternative techniques drawn from the fields of resistant, robust and non-parametric
statistics are usually much less affected by the presence of 'outliers'
and other forms of non-normality. Some of the theoretical basis for the
alternative techniques is presented as motivation for their use and to
provide quantitative measures for their performance as compared with the
traditional techniques that they may replace. Although this work is by
no means exhaustive, typically a couple of suitable alternatives are presented
for each of the common statistical quantities/tests mentioned above. All
of the technical details needed to apply these techniques are presented
in an extensive appendix.
With regard to the issue of homogeneity of the climate record, a powerful
non-parametric technique is introduced for the objective identification
of 'change-points' (discontinuities) in the mean. These may arise either
naturally (abrupt climate change) or as the result of errors or changes
in instruments, recording practices, data transmission, processing, etc.
The change-point test is able to identify multiple discontinuities and
requires no 'metadata' or comparison with neighbouring stations; these
are important considerations because instrumental changes are not always
documented and, particularly with regard to radiosonde observations, suitable
neighbouring stations for 'buddy checks' may not exist. However, when such
auxiliary information is available it may be used as independent confirmation
of the artificial nature of the discontinuities.
The application and practical advantages of these alternative techniques
are demonstrated using primarily actual radiosonde station data and in
a few cases using some simulated (artificial) data as well. The ease with
which suitable examples were obtained from the radiosonde archive begs
for serious consideration of these techniques in the analysis of climate
data.