Please choose from the following:
"Confidence Intervals. A practical compromise is to estimate
the variance pointwise and construct 2 standard error bars around the estimate.
. . Such an interval is not a confidence interval for the unknown density function
but rather a confidence interval for the nonparametric estimate." (Scott, 1992,
p. 259).
The Geographic Reference Distribution
One of the recent developments in small-area studies is
the computation of geographical reference distributions which permit the evaluation
of local measures of disease incidence as well as the relationship of disease
incidences to socio-economic factors as well as age and sex. The reference distribution
shows how the typical pattern of the measured disease rate in a given local
situation might vary if it is consistent with a given hypothesis. For example,
it is common to hypothesize that the likelihood of a person having a disease
is given by the proportion of individuals in their age and sex group who, in
the larger region, have the disease. These reference distributions are usually
computed using Monte Carlo simulation methods, although, if the hypothesis is
simple, they sometimes can be computed analytically. An example is where the
expectation of a disease is a constant ratio of the population, in which case
the binomial distribution for the given sample size, describes the distribution
of expected values.
The value of the geographical reference distribution is
that the typical patterns of disease rates at any location will reflect the
particular age and sex distribution in that location. If the sample patterns
are measured at adjacent locations and share simulated observations in common,
the reference distribution will also, similarly, share observations.
Test Graph Method: a method, devised by Silverman (1978),
to illustrate how density changes with window width for any given sample size
when a probability density function is estimated using the kernel method from
independent identically distributed simulated observations. There is subjectivity
in the analysis of test graphs--which are contour plots for the two-dimensional
case. Silverman concludes (p. 7) that "it may not be a very good idea to use
the test graph alone for choosing the window width for multivariate data; however,
the method may be very useful for checking that a chosen window width is sensible."
due to Silverman (..88)
The method requires the consideration of 'test surfaces'
giving plots of ....
p. 89 Nearly all package programs for finding contour diagrams
and perspective views of functions require, as input, an array giving the value
of the function at each point of a regular grid. Computation time is reduced
if, from each grid point, the events are stored in order of their distances
from each grid point.