bootMSD : Parametric bootstrap for median scaled difference

Description

Generates a parametric bootstrap for the median of scaled differences from each point in a data set to all other points..

Usage

bootMSD(x, ...)
        # S3 method for default
bootMSD(x, s = mad, B = 3000, probs = c(0.95, 0.99), 
                method = c("rnorm", "lhs"), keep = FALSE, labels = names(x), ...)
        # S3 method for MSD
bootMSD(x, B = 3000, probs = c(0.95, 0.99), 
                method = c("rnorm", "lhs"), keep = FALSE, labels = names(x), ...)

Value

An object of class "bootMSD", consisting of a vector of length length(x) of median scaled absolute deviations for each observation, with attributes:

msd: vector of raw calculated MSD values calculated by msd
labels: character vector of labels, by default taken from x
probs: vextor of probabilities supplied and used for quantiles
critical.values: matrix of quantiles. Each row corresponds to a probability in probs and each column to an individual data point.
pvals: p-values estimated as the observed proportion of simulated values exceeding the MSD value calculated by msd.
B: Number of bootstrap replicates used.
method: The sampling method used by the parametric bootstrap.
t: If keep == TRUE, the individual bootstrap replicates generated by bootMSD. Set to NA if keep == FALSE.

Summary, print and plot methods are provided for the class; see bootMSD-class.

Arguments

x: An R object. For the default method, a vector of observations. For the MSD method, an object of class "MSD". For print, summary and plot methods, an object of class "bootMSD".
s: Either a function returning an estimate of scale for x or a vector of length length(x) of standard errors or standard uncertainties in x.
B: Scalar number of bootstrap replicates.
probs: Vector of probabilities at which to calculate upper quantiles. Passed to quantile.
method: Character value describing the simulation method.
keep: If keep == TRUE the individual bootstrap replicates are retained.
labels: Character vector of labels for individual values.
...: Parameters passed to other methods.

Author

S. L. R. Ellison s.ellison@lgcgroup.com

Details

bootMSD calculates a parametric bootstrap simulation (or Monte carlo simulation) of the results of msd applied to data. This allows individual case-specific quantiles and p-values to be estimated that allow for different standard errors (or standard uncertainties) s.

The sampling method is currently either sampling from rnorm or by latin hypercube sampling using lhs.

Individual upper quantiles for probabilities probs and p-values are estimated directly from the bootstrap replicates. Quantiles use quantile. p-values are estimated from the proportion of replicates that exceed the observed MSD calculated by msd. Note that the print method for the summary object does not report zero proportions as identically zero.

References

Ellison, S. L. R. (2018) An outlier-resistant indicator of anomalies among inter-laboratory comparison data with associated uncertainty. _Metrologia_ (accepted 4 October 2018)

Examples

Run this code


  data(Pb)
  if (FALSE) {
  #Default method:
  set.seed(1023)
  boot.Pb.default <- bootMSD(Pb$value, Pb$u)  # Uses individual standard uncertainties
  summary(boot.Pb.default)
  
  
  #Method for MSD object:
  msd.Pb<-msd(Pb$value, Pb$u)  # Uses individual standard uncertainties
  boot.Pb <- bootMSD(msd.Pb, B=5000)
  	#Increased replication compared to default
  summary(boot.Pb)
  
  # NOTE: The default summary gives individual observation p-values. 
  # To correct for multiple comparisons, apply 
  # a suitable p-value adjustment:
  summary(boot.Pb, p.adjust="holm")

  }

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