N1 Consider the database "LakeHuron" , containing the annual measurements
of the level (in feet) of Lake Huron 1875{1972, see
https://stat.ethz.ch/R-manual/Rdevel/library/datasets/html/LakeHuron.html.
The general aim is to estimate the probability density of the level of the
lake.
(i) Construct the histogram estimator with the number of bins selected
by the Sturges rule. On the same plot display the graph of the density of
the normal distribution with estimated mean and standard
deviation (normal fit).
(ii) Among the histograms with the number of bins from 5 to 30, find
the histogram estimator which is closest to the normal fit. Comment on the
bias-variance tradeoff in this case.
(iii) Construct the kernel estimators with various kernels (apply all
kernels available in the R language). The bandwidth can be chosen by
default. Construct the kernel estimators under various choices of
bandwidth (apply all rules for bandwidth selection, which are implemented
in the R language, the kernel can be chosen by default).
Among all constructed kernel estimators, find the kernel estimator
which is closest to the normal fit
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