nag_outlier_peirce_two_var (g07gbc) tests a potential outlying value using Peirce's criterion. Let
- denote a vector of residuals with mean zero and variance obtained from fitting some model to a series of data ,
- denote the largest absolute residual in , i.e., for all , and let denote the data series with the observation corresponding to having been omitted,
- denote the residual variance on fitting model to ,
- denote the ratio of and with .
Peirce's method flags
as a potential outlier if
, where
and
is obtained from the solution of
where
and
is the cumulative distribution function for the standard Normal distribution.
Unlike
nag_outlier_peirce (g07gac), both
and
must be supplied and therefore no assumptions are made about the nature of the relationship between these two quantities. Only a single potential outlier is tested for at a time.
This function uses an algorithm described in
nag_opt_one_var_no_deriv (e04abc) to refine a lower,
, and upper,
, limit for
. This refinement stops when
or
.
Gould B A (1855) On Peirce's criterion for the rejection of doubtful observations, with tables for facilitating its application The Astronomical Journal 45
Not applicable.
None.
This example reads in a series of values and variances and checks whether each is a potential outlier.
The dataset used is from Peirce's original paper and consists of fifteen observations on the vertical semidiameter of Venus. Each subsequent line in the dataset, after the first, is the result of dropping the observation with the highest absolute value from the previous data and recalculating the variance.