  In this article, we considered the problem of sea ice cover is melting.
Considering the `satellite passive microwave remote sensing data' as functional
data, we studied daily observation of sea ice cover of each year as a smooth
continuous function of time. We investigated the mean function for the sea ice
area for following decades and computed the corresponding $95\%$ bootstrap
confidence interval for the both Arctic and Antarctic Oceans. We found the mean
function for the sea ice area dropped statistically significantly in recent
decades for the Arctic Ocean. However, no such statistical evidence was found
for the Antarctic ocean. Essentially, the mean function for sea ice area in the
Antarctic Ocean is unchanged. Additional evidence of the melting of sea ice
area in the Arctic Ocean is provided by three types of phase curve (namely,
Area vs. Velocity, Area vs. Acceleration, and Velocity Vs. Acceleration). In
the Arctic Ocean, during the summer, the current decades is observing the size
of the sea ice area about $30\%$ less, than what it used to be during the first
decade. In this article, we have taken a distribution-free approach for our
analysis, except the data generating process, belongs to the Hilbert space.
