| Summary: | <p>The nonparametric confidence interval for an unknown function is quite a useful tool
in statistical inferential procedures; and thus, there exists a wide body of literature on the
topic. The primary issues are the smoothing parameter selection using an appropriate criterion
and then the coverage probability and length of the associated confidence interval.
Here our focus is on the interval length in general and, in particular, on the variability in the
lengths of nonparametric intervals for probability density and hazard rate functions. We
start with the analysis of a nonparametric confidence interval for a probability density function
noting that the confidence interval length is directly proportional to the square root of a
density function. That is variability of the length of the confidence interval is driven by the
variance of the estimator used to estimate the square-root of the density function. Therefore
we propose and use a kernel-based constant variance estimator of the square-root of a
density function. The performance of confidence intervals so obtained is studied through
simulations. The methodology is then extended to nonparametric confidence intervals for
the hazard rate function.</p>
<p>
Changing direction somewhat, the second part of this thesis presents a statistical study
of daily snow trends in the United States and Canada from 1960-2009. A storage model
balance equation with periodic features is used to describe the daily snow depth process.
Changepoint (inhomogeneities features) are permitted in the model in the form of mean
level shifts. The results show that snow depths are mostly declining in the United States.
In contrast, snow depths seem to be increasing in Canada, especially in north-western areas
of the country. On the whole, more grids are estimated to have an increasing snow trend
than a decreasing trend. The changepoint component in the model serves to lessen the
overall magnitude of the trends in most locations. </p>
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