Description Usage Arguments Value References See Also Examples
Performs maximum trimmed likelihood estimation by the fasttle algorithm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  fasttle(Idt,
CovCase=1:4,
SelCrit=c("BIC","AIC"),
alpha=control@alpha,
nsamp = control@nsamp,
seed=control@seed,
trace=control@trace,
use.correction=control@use.correction,
ncsteps=control@ncsteps,
getalpha=control@getalpha,
rawMD2Dist=control@rawMD2Dist,
MD2Dist=control@MD2Dist,
eta=control@eta,
multiCmpCor=control@multiCmpCor,
getkdblstar=control@getkdblstar,
outlin=control@outlin,
trialmethod=control@trialmethod,
m=control@m,
reweighted = control@reweighted,
otpType=control@otpType,
control=RobEstControl(), ...)

Idt 
An IData object representing intervalvalued entities. 
CovCase 
Configuration of the variancecovariance matrix: a set of integers between 1 and 4. 
SelCrit 
The model selection criterion. 
alpha 
Numeric parameter controlling the size of the subsets over which the trimmed likelihood is maximized; roughly alpha*nrow(Idt) observations are used for computing the trimmed likelihood. Note that when argument ‘getalpha’ is set to “TwoStep” the final value of ‘alpha’ is estimated by a twostep procedure and the value of argument ‘alpha’ is only used to specify the size of the samples used in the first step. Allowed values are between 0.5 and 1. 
nsamp 
Number of subsets used for initial estimates. 
seed 
Initial seed for random generator, like 
trace 
Logical (or integer) indicating if intermediate results should be printed; defaults to 
use.correction 
whether to use finite sample correction factors; defaults to 
ncsteps 
The maximum number of concentration steps used each iteration of the fasttle algorithm. 
getalpha 
Argument specifying if the ‘alpha’ parameter (roughly the percentage of the sample used for computing the trimmed likelihood) should be estimated from the data, or if the value of the argument ‘alpha’ should be used instead. When set to “TwoStep”, ‘alpha’ is estimated by a twostep procedure with the value of argument ‘alpha’ specifying the size of the samples used in the first step. Otherwise, with the value of argument ‘alpha’ is used directly. 
rawMD2Dist 
The assumed reference distribution of the raw MCD squared distances, which is used to find to cutoffs defining the observations kept in onestep reweighted MCD estimates. Alternatives are ‘ChiSq’,‘HardRockeAsF’ and ‘HardRockeAdjF’, respectivelly for the usual Quisquared, and the asymptotic and adjusted scaled F distributions proposed by Hardin and Rocke (2005). 
MD2Dist 
The assumed reference distributions used to find cutoffs defining the observations assumed as outliers. Alternatives are “ChiSq” and “CerioliBetaF” respectivelly for the usual Quisquared, or the Beta and F distributions proposed by Cerioli (2010). 
eta 
Nominal size for the null hypothesis that a given observation is not an outlier. Defines the raw MCD Mahalanobis distances cutoff used to choose the observations kept in the reweightening step. 
multiCmpCor 
Whether a multicomparison correction of the nominal size (eta) for the outliers tests should be performed. Alternatives are: ‘never’ – ignoring the multicomparisons and testing all entities at ‘eta’ nominal level. ‘always’ – testing all n entitites at 1. (1.‘eta’^(1/n)); and ‘iterstep’ – use the iterated rule proposed by Cerioli (2010), i.e., make an initial set of tests using the nominal size 1. (1‘eta’^(1/n)), and if no outliers are detected stop. Otherwise, make a second step testing for outliers at the ‘eta’ nominal level. 
getkdblstar 
Argument specifying the size of the initial small (in order to minimize the probability of outliers) subsets. If set to the string “Twopplusone” (default) the initial sets have twice the number of intervalvalue variables plus one (i.e., they are the smaller samples that lead to a nonsingular covariance estimate). Otherwise, an integer with the size of the initial sets. 
outlin 
The type of outliers to be considered. “MidPandLogR” if outliers may be present in both MidPpoints and LogRanges, “MidP” if outliers are only present in MidPpoints, or “LogR” if outliers are only present in LogRanges. 
trialmethod 
The method to find a trial subset used to initialize each replication of the fasttle algorithm. The current options are “simple” (default) that simply selects ‘kdblstar’ observations at random, and “Poolm” that divides the original sample into ‘m’ nonoverlaping subsets, applies the ‘simple trial’ and the refinement methods to each one of them, and merges the results into a trial subset. 
m 
Number of nonoverlaping subsets used by the trial method when the argument of ‘trialmethod’ is set to 'Poolm'. 
reweighted 
Should a (Re)weighted estimate of the covariance matrix be used in the computation of the trimmed likelihood or just a “raw” covariance estimate; default is (Re)weighting. 
otpType 
The amount of output returned by fasttle. Current options are “SetMD2andEst” (default) which returns an ‘IdtSngNDRE’ object with the fasttle estimates, 
control 
a list with estimation options  this includes those above provided in the function specification. See

... 
Further arguments to be passed to internal functions of 
An object of class IdtE
with the fasttle estimates, the value of the comparison criterion used to select the covariance configurations, the robust squared Mahalanobis distances, and optionally (if argument ‘otpType’ is set to true) performance statistics concerning the algorithm execution.
Brito, P., Duarte Silva, A. P. (2012), Modelling Interval Data with Normal and SkewNormal Distributions. Journal of Applied Statistics 39(1), 3–20.
Cerioli, A. (2010), Multivariate Outlier Detection with HighBreakdown Estimators.
Journal of the American Statistical Association 105 (489), 147–156.
Duarte Silva, A.P., Filzmoser, P. and Brito, P. (2017), Outlier detection in interval data. Advances in Data Analysis and Classification, 1–38.
Hadi, A. S. and Luceno, A. (1997), Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms.
Computational Statistics and Data Analysis 25(3), 251–272.
Hardin, J. and Rocke, A. (2005), The Distribution of Robust Distances.
Journal of Computational and Graphical Statistics 14, 910–927.
Todorov V. and Filzmoser P. (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software 32(3), 1–47.
fulltle
, RobEstControl
, getIdtOutl
, IdtSngNDRE
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  ## Not run:
# Create an IntervalData object containing the intervals of temperatures by quarter
# for 899 Chinese meteorological stations.
ChinaT < IData(ChinaTemp[1:8])
# Estimate parameters by the fast trimmed maximum likelihood estimator,
# using a twostep procedure to select the triming parameter, a reweighted
# MCD estimate, and the classical 97.5% chisquared quantile cutoffs.
Chinafasttle1 < fasttle(ChinaT)
cat("China maximum trimmed likelihood estimation results =\n")
print(Chinafasttle1)
# Estimate parameters by the fast trimmed maximum likelihood estimator, using
# the triming parameter that maximizes breakdown, and a reweighted MCD estimate
# based on the 97.5% quantiles of Hardin and Rocke adjusted F distributions.
Chinafasttle2 < fasttle(ChinaT,alpha=0.5,getalpha=FALSE,rawMD2Dist="HardRockeAdjF")
cat("China maximum trimmed likelihood estimation results =\n")
print(Chinafasttle2)
# Estimate parameters by the fast trimmed maximum likelihood estimator, using a twostep procedure
# to select the triming parameter, a reweighted MCD estimate based on Hardin and Rocke adjusted
# F distributions, and 95% quantiles, and the Cerioli Beta and F distributions together
# with Cerioli iterated procedure to identify outliers in the first step.
Chinafasttle3 < fasttle(ChinaT,rawMD2Dist="HardRockeAdjF",eta=0.05,MD2Dist="CerioliBetaF",
multiCmpCor="iterstep")
cat("China maximum trimmed likelihood estimation results =\n")
print(Chinafasttle3)
## End(Not run)

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