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Keywords:

  • Functional data analysis;
  • Ionosphere;
  • Spatial statistics;
  • Two-sample problem

Summary.  The paper develops a significance test for evaluating the equality of the mean functions in two samples of spatially indexed functional data. The problem is motivated by an important question in space physics research which is related to the hypothesis of ionospheric global cooling (as opposed to the conjectured global warming of near surface atmosphere). The critical electron frequency of the ionosphere's F2 region, foF2, can be used to test conjectures about the trends in the ionosphere empirically. We apply the proposed test to the foF2-records over eastern and western Europe to verify whether there is a conjectured difference between first-order behaviour of these records over regions with different magnetic inclinations. It is found that the difference between the means is statistically significant for night-time records. The implications of this result are discussed. Finite sample performance of the test proposed is validated via numerical simulations.