fasttle-methods {MAINT.Data}

Methods for Function fasttle in Package ‘MAINT.Data’

Description

Performs maximum trimmed likelihood estimation by the fasttle algorithm

Usage

fasttle(Sdt,
    CovCase=1:4,
    SelCrit=c("BIC","AIC"),
    alpha=control@alpha,
    nsamp = control@nsamp,
    seed=control@seed,
    trace=control@trace,
    use.correction=[e-mail],
    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,
    k2max = control@k2max, 
    otpType=control@otpType,
    control=RobEstControl(), ...)

Arguments

Sdt

An IData object representing interval-valued units.

CovCase

Configuration of the variance-covariance 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(Sdt) 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 two-step 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 .Random.seed, see rrcov.control.

trace

Logical (or integer) indicating if intermediate results should be printed; defaults to FALSE.

use.correction

whether to use finite sample correction factors; defaults to TRUE.

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 two-step procedure with the value of argument ‘alpha’ specifying the size of the samples used in the first step. Otherwise, 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 one-step reweighted MCD estimates. Alternatives are ‘ChiSq’,‘HardRockeAsF’ and ‘HardRockeAdjF’, respectivelly for the usual Chi-square, 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 Chi-square, 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 interval-value variables plus one (i.e., they are the smaller samples that lead to a non-singular 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’ non-overlaping 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 non-overlaping 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.

k2max

Maximal allowed l2-norm condition number for correlation matrices. Correlation matrices with condition number above k2max are considered to be numerically singular, leading to degenerate results.

otpType

The amount of output returned by fasttle. Current options are “SetMD2andEst” (default) which returns an ‘IdtSngNDRE’ object with the fasttle estimates,
a vector with the final trimmed subset elements used to compute these estimates and the corresponding robust squared Mahalanobis distances, and
“SetMD2EstandPrfSt” wich returns an ‘IdtSngNDRE’ object with the previous slots plust a list of some performance statistics concerning the algorithm execution.

control

a list with estimation options - this includes those above provided in the function specification. See RobEstControl for the defaults. If control is supplied, the parameters from it will be used. If parameters are passed also in the invocation statement, they will override the corresponding elements of the control object.

...

Further arguments to be passed to internal functions of fasttle.

Value

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.

References

Brito, P., Duarte Silva, A. P. (2012), Modelling Interval Data with Normal and Skew-Normal Distributions. Journal of Applied Statistics 39(1), 3–20.

Cerioli, A. (2010), Multivariate Outlier Detection with High-Breakdown 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.

See Also

fulltle, RobEstControl, getIdtOutl, IdtSngNDRE

Examples

## Not run: 

# Create an Interval-Data 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 two-step procedure to select the trimming parameter, a reweighted 
# MCD estimate, and the classical 97.5% chi-square quantile cut-offs.

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 two-step procedure
# to select the triming parameter, a reweighed 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)