Detection of Changes in Mean of Vectors with Application to Hydrology
Daniela Jaruskova
Mathematics, Czech Technical University, Faculty of Civil Engineering, Prague, Czech Republic

When we study possible trends in precipitation series, the main effect of global warming may not be a decrease or increase of annual means but rather a change of distribution of precipitation in a year. As a consequence behavior of discharges during a calendar year may change as well. If the behavior during a year is described by monthly averages, the goal of statistical inference is to detect a change in mean of twelve-dimensional vectors with dependent components, see Horvath et al (1999) and Jaruskova (2010). Often it seems more natural to describe the behavior during a year by daily averages. However here, we encounter a problem that the number of components of studied vectors is larger than the number of observed vectors. In such a case application of the method of principal components is recommended, for more details see Benko et al. (2009) and Berkes et al. (2009). In our contribution we would like to present test procedures for detecting changes in vector means and discuss their advantages and disadvantages.


Benko M., Haerdle W., Kneip A.: Common functional principal components. Annals of Statistics 37, 2009, 1 – 34.

Berkes I., Gabrys R., Horvath L., Kokoszka P.: Detecting changes in the mean of functional observations. JRSS B 71, 2009, 927 – 946.

Horvath L., Kokoszka P., Steinebach J.: Testing for changes in multivariate dependent observations with an application to temperature changes. Journal of Multivariate Analysis 68, 1999, 96 - 119.

Jaruskova D.: Asymptotic behavior of a test statistic for detection of change in mean of vectors. JSPI 140, 2010, 616 - 625.

Keywords: change point analysis; change in mean vector; hypotheses testing

Biography: Daniela Jaruskova is professor of mathematics at the Czech Technical University. For more than twenty years she has been interested in change point analysis and its application to environmental studies.