stability.plot: Stability plot

In envoutliers: Methods for Identification of Outliers in Environmental Data

Description

A stability plot for maximum likelihood or moment estimates of the GP parameters (Coles, 2001), including confidence intervals, at a range of thresholds or number of the largest observations.

Usage

stability.plot(x, umin = quantile(na.omit(x), probs = 0.8),
  umax = quantile(na.omit(x), probs = 0.95),
  kmin = round(length(na.omit(x)) * 0.05),
  kmax = round(length(na.omit(x)) * 0.2), nint = 100, conf = 0.95,
  est.method = "mle", u0 = NULL, k0 = NULL)

Arguments

x	data values. Supported data types a numeric vector a time series object ts a time series object xts a time series object zoo
umin	the minimum threshold at which the mean residual life function is calculated. Default is umin = quantile(na.omit(x), probs = 0.8).
umax	the maximum threshold at which the mean residual life function is calculated. Default is ummax = quantile(na.omit(x), probs = 0.95).
kmin	the minimum number of largest order statistics for which the mean residual life function is calculated based on moment estimates. Default is kmin = round(length(na.omit(x)) * 0.05).
kmax	the maximum number of largest order statistics for which the mean residual life function is calculated based on moment estimates. Default is kmax = round(length(na.omit(x)) * 0.2).
nint	the number of points at which the mean residual life function is calculated. Default is nint = 100.
conf	the confidence coefficient for the confidence intervals depicted in the plot. Default is conf = 0.95.
est.method	a character string specifying the type of estimates for the scale and shape parameters of GP distribution. Possible options are "mle" (default) to use maximum likelihood estimates (Coles, 2001) "moment" to use moment estimates (de Haan and Ferreira, 2006).
u0	a numeric value giving the threshold meant for a GP approximation of the threshold exceedances. Default is u0 = NULL.
k0	a numeric value giving the number (k0-1) of largest observations meant for a GP approximation. Default is k0 = NULL.

Details

The function estimates the GP parameters at a range of thresholds (in case est.method = "mle") or a range of upper order statistics (in case of est.method = "moment"), and shows the sample paths of the estimates. The estimates of the shape or the scale parameter are expected to be constant or to change linearly, respectively, with threshold levels at which the GP model is appropriate. If u0 (or k0, respectively) is given, a threshold-dependency lines for the particular parameters are plotted in addition. The lines provide the user an option to assess the suitability of u0 or k0 as a lower bound for the threshold exceedances (for u0) or the number of upper order statistics (for k0) to fit the GP distribution. In case est.method = "mle" and u0 takes a value, the theoretical dependency lines for the parameters are evaluated on the basis of MLE estimates. For the case est.method = "moment" and k0 is given, the dependency lines are estimated using the moment estimators. In case est.method = "moment" the value x(n-k) on the x-axis of MRL plot denotes the (k + 1)-th largest observation of the total number of n observations.

References

Theo Gasser, Alois Kneip & Walter Koehler (1991) A flexible and fast method for automatic smoothing. Journal of the American Statistical Association 86, 643-652. https://doi.org/10.2307/2290393

E. Herrmann (1997) Local bandwidth choice in kernel regression estimation. Journal of Graphical and Computational Statistics 6, 35-54.

Herrmann E, Maechler M (2013). lokern: Kernel Regression Smoothing with Local or Global Plug-in Bandwidth. R package version 1.1-5, URL http://CRAN.R-project.org/package=lokern.

Gasser, T, Muller, H-G, Mammitzsch, V (1985). Kernels for nonparametric curve estimation. Journal of the Royal Statistical Society, B Met., 47(2), 238-252.

Coles, S (2001). An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London, U.K., 208pp.

de Haan, L, Ferreira, A (2006). Extreme Value Theory: An Introduction. Springer.

Examples

data("mydata", package = "openair")
x = mydata$o3[format(mydata$date, "%m %Y") == "12 2002"]
res = smoothing(y = x)$residuals
stability.plot(res)

envoutliers documentation built on July 2, 2020, 3:25 a.m.