Methods for Function fasttle in Package ‘MAINT.Data’
Description
Performs maximum trimmed likelihood estimation by the fasttle algorithm
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  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,
getkdblstar=control@getkdblstar,
outlin=control@outlin,
trialmethod=control@trialmethod,
m=control@m,
reweighted = control@reweighted,
otpType=control@otpType,
control=RobEstControl(), ...)

Arguments
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*Idt@NIVar observations are used for computing the trimmed likelihood. Allowed values are between 0.5 and 1. 
nsamp 
Number of subsets used for initial estimates. 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. 
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. 
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 “OnlyEst” (default) where only an ‘IdtE’ object with the fasttle estimates is returned, 
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 
Value
If argument ‘otpType’ is set to “OnlyEst”, an object of class ‘IdtE’ with the fasttle estimates, their loglikelihood values, and the value of the comparison criterion used to select the covariance configurations.
If argument ‘otpType’ is set to “SetMD2andEst” a list with the following components:
sol 
An object of class ‘IdtE’ with the fasttle estimates, their loglikelihood values, and the value of the comparison criterion used to select the covariance configurations. 
Set 
A vector with the final trimmed subset elements used to compute the fasttle estimates. 
RobMD2 
A vector with the robust squared Mahalanobis distances used to select the trimmed subset. 
If argument ‘otpType’ is set to “SetMD2EstandPrfSt” a list with the following components:
sol 
An object of class ‘IdtE’ with the fasttle estimates, their loglikelihood values, and the value of the comparison criterion used to select the covariance configurations. 
Set 
A vector with the final trimmed subset elements used to compute the fasttle estimates. 
RobMD2 
A vector with the robust squared Mahalanobis distances used to select the trimmed subset. 
PerfSt 
A a list with the following components: 
Methods
signature(Idt = "IData")

Performs maximum trimmed likelihood estimation for intervalvalued data using the fasttle algorithm, assuming a Gaussian distribution, and considering alternative variancecovariance matrix configurations
References
Brito, P., Duarte Silva, A. P. (2012), Modelling Interval Data with Normal and SkewNormal Distributions. Journal of Applied Statistics 39(1), 3–20.
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.
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
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14  ## 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 using the fast trimmed maximum likelihood estimator, and assuming that one of
# the C2, C3 or C4 restricted Covariance Cases holds
Chinafasttle < fasttle(ChinaT,CovCase=2:4)
cat("China maximum trimmed likelihood estimation results =\n")
print(Chinafasttle)
## End(Not run)

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