Methods for Function fasttle in Package ‘MAINT.Data’

Description

Performs maximum trimmed likelihood estimation by the fasttle algorithm

Usage

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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 interval-valued entities.

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*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 two-step 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 .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, 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 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.

otpType

The amount of output returned by fasttle. Current options are “OnlyEst” (default) where only an ‘IdtE’ object with the fasttle estimates is returned,
“SetMD2andEst” which returns a list with an ‘IdtE’ object of 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 a list with the previous three components 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

If argument ‘otpType’ is set to “OnlyEst”, an object of class ‘IdtE’ with the fasttle estimates, their log-likelihood 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 log-likelihood 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 log-likelihood 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:
RepSteps: A list with one component by Covariance Configuration, containing a vector with the number of refinement steps performed by the fasttle algorithm by replication.
RepLogLik: A list with one component by Covariance Configuration, containing a vector with the best log-likelihood found be fasttle algorithm by replication.
StpLogLik: A list with one component by Covariance Configuration, containing a matrix with the evolution of the log-likelihoods found be fasttle algorithm by replication and refinement step.

Methods

signature(Idt = "IData")

Performs maximum trimmed likelihood estimation for interval-valued data using the fasttle algorithm, assuming a Gaussian distribution, and considering alternative variance-covariance matrix configurations

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.

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

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## 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 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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